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laboutique.edpsciences.fr-R001859 03 01 01 R001859 00 ED E107 00 01 01 Global Well-Posedness for Some Fluid Models 01 eng 08 294 03 22 2824415 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20230216 02 01 002222 03 9782759829064 15 9782759829064 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-002222 03 01 01 002222 03 9782759829064 15 9782759829064 10 EA E107 10 00 01 R001859 ED E107 1 10 01 02 Current Natural Sciences 01 01 Global Well-Posedness for Some Fluid Models 1 A01 01 A2052 Yuming Qin Qin, Yuming Yuming Qin Dr. Yuming QIN is full professor, head of Mathematics Department and director of Institute of Nonlinear Sciences of Donghua University. His research interests are global (local) wellposedness of solutions and infinite-dimensional dynamical systems for nonlinear evolutionary equations including fluid equations such as Navier–Stokes equations, MHD, etc, and thermo(visco)elasticequations.<o:p></o:p> 2 A01 01 A2110 Jianlin ZHANG ZHANG, Jianlin Jianlin ZHANG Dr. Jianlin ZHANG is associate Professor in College of Science, Zhongyuan University of Technology since 2012. 01 eng 08 292 03 01 24 Izibook:Subject Mathématiques 24 Izibook:SubjectAndCategoryAndTags |Mathématiques| 20 mathematics;well-posedness;fluid models;radiation hydrodynamics;Navier-Stokes equations;Newtonian fluid-model. 10 2011 MAT007020 01 510 05 06 03 00 This book presents recent results on global well-posedness including asymptotic behavior of global solutions to some fluid models, such as combustion model of radiative gas, radiation hydrodynamics model, Navier-Stokes equations with capillary and p-th power Newtonian fluid model. These models have the similar structures, which consist of Navier-Stokes equations coupled with other equation or with other effects. Results collected in this book are established by the authors and their collaborators in recent years. 02 00 This book presents recent results on global well-posedness including asymptotic behavior of global solutions to some fluid models, such as combustion model of radiative gas, radiation hydrodynamics model, Navier-Stokes equations with capillary and p-th power Newtonian fluid model. 04 00 Foreword................................................... IX<o:p></o:p>CHAPTER 1<o:p></o:p>Preliminary................................................. 1<o:p></o:p>1.1 Sobolev Spaces and Their Basic Properties..................... 1<o:p></o:p>1.1.1 Weak Derivatives and Their Properties.................. 1<o:p></o:p>1.1.2 Sobolev Spaces..................................... 4<o:p></o:p>1.1.3 Some Properties of Sobolev Spaces...................... 5<o:p></o:p>1.2 Some Inequalities in Analysis............................... 12<o:p></o:p>1.2.1 The Young Inequality................................ 12<o:p></o:p>1.2.2 The Poincaré Inequality.............................. 13<o:p></o:p>1.2.3 The Bellman–Gronwall Inequality...................... 13<o:p></o:p>1.2.4 The Hölder Inequality............................... 14<o:p></o:p>1.2.5 The Minkowski Inequality............................ 15<o:p></o:p>1.2.6 The Jensen Inequality............................... 15<o:p></o:p>1.2.7 The Shen–Zheng Inequality........................... 16<o:p></o:p>1.2.8 The Interpolation Inequality........................... 19<o:p></o:p>1.2.9 The Gagliardo–Nirenberg Interpolation Inequality .......... 19<o:p></o:p>1.3 C0-Semigroup........................................... 20<o:p></o:p>CHAPTER 2<o:p></o:p>Global Existence and Exponential Stability of Spherically Symetric Solutions to a Compressible Combustion Radiative and Reactive Gas ...... 232.1 Introduction............................................ 23<o:p></o:p>2.2 Model and Main Results................................... 24<o:p></o:p>2.2.1 Combustion Model of Radiative and Reactive Gas .......... 24<o:p></o:p>2.2.2 Spherical Symmetry Model of Combustion Model ........... 25<o:p></o:p>2.2.3 Main Theorems.................................... 28<o:p></o:p>2.3 Global Existence and Exponential Stability in H1 ................ 30<o:p></o:p>2.3.1 Global Existence of Solutions in H1..................... 31<o:p></o:p>2.3.2 Exponential Stability of Solutions in H1.................. 55<o:p></o:p>2.4 Global Existence and Exponential Stability in H2 ................ 67<o:p></o:p>2.4.1 Global Existence of Solutions in H2..................... 67<o:p></o:p>2.4.2 Exponential Stability of Solutions in H2.................. 74<o:p></o:p>2.5 Global Existence and Exponential Stability in H4 ................ 75<o:p></o:p>2.5.1 Global Existence of Solutions in H4..................... 75<o:p></o:p>2.5.2 Exponential Stability of Solutions in H4.................. 87<o:p></o:p>2.6 Bibliographic Comments................................... 90<o:p></o:p>CHAPTER 3<o:p></o:p>Global Existence, Uniqueness and Exponential Stability of Solutions for the One-Dimensional Navier–Stokes Equations with Capillarity ........ 933.1 Introduction............................................ 93<o:p></o:p>3.2 Model and Main Results................................... 94<o:p></o:p>3.2.1 Korteweg-Type Model............................... 94<o:p></o:p>3.2.2 Main Theorems.................................... 97<o:p></o:p>3.3 Global Existence and Exponential Stabilityin H1 þ ............... 993.3.1 Global Existence in H1 þ .............................. 993.3.2 Asymptotic Behavior in H1 þ ........................... 1143.3.3 Exponential Stability in H1 þ ........................... 1203.4 Global Existence and Exponential Stabilityin H2 þ ............... 1223.4.1 Global Existence and Uniqueness in H2 þ .................. 1223.4.2 Exponential Stability in H2 þ ........................... 1253.5 Global Existence and Exponential Stabilityin H4 þ ............... 1263.5.1 Global Existence in H4 þ .............................. 1263.5.2 Asymptotic Behavior of Solutions in H4 þ ................. 1323.5.3 Exponential Stability in H4 þ ........................... 1343.6 Bibliographic Comments................................... 137<o:p></o:p>CHAPTER 4<o:p></o:p>Exponential Stability of Solutions for theCompressible p-th Power Newtonian Fluid with Large Initial Data........................... 1394.1 Introduction............................................ 139<o:p></o:p>4.2 Model and Main Results................................... 140<o:p></o:p>4.3 Global Existence and Exponential Stability in H1 ................ 143<o:p></o:p>4.3.1 Global Existence in H1 ...............................143<o:p></o:p>4.3.2 Exponential Stability in H1........................... 162<o:p></o:p>4.4 Global Existence and Exponential Stability in H2 ................ 163<o:p></o:p>4.5 Global Existence and Exponential Stability in H4 ................ 165<o:p></o:p>4.6 Bibliographic Comments................................... 166<o:p></o:p>CHAPTER 5<o:p></o:p>Global Existence and Asymptotic Behavior of Spherically Symetric Solutions for the Multi-Dimensional Infrarelativistic Model .............. 1695.1 Introduction............................................ 169<o:p></o:p>5.2 Reformulation and Main Theorems........................... 171<o:p></o:p>5.2.1 Reformulation of Model.............................. 171<o:p></o:p>5.2.2 Main Theorems.................................... 174<o:p></o:p>5.3 Global Existence and Asymptotic Behavior in H1 ................ 177<o:p></o:p>5.3.1 Global Existence in H1............................... 177<o:p></o:p>5.3.2 Asymptotic Behavior in H1........................... 196<o:p></o:p>5.4 Global Existence and Asymptotic Behavior inH2 ................ 201<o:p></o:p>5.4.1 Global Existence in H2............................... 201<o:p></o:p>5.4.2 Asymptotic Behavior in H2........................... 205<o:p></o:p>5.5 Global Existence and Asymptotic Behavior in H4 ................ 206<o:p></o:p>5.5.1 Global Existence in H4............................... 206<o:p></o:p>5.5.2 Asymptotic Behavior in H4........................... 219<o:p></o:p>5.6 Bibliographic Comments................................... 221<o:p></o:p>CHAPTER 6<o:p></o:p>Global Existence and Asymptotic Behavior ofCylindrically Symetric Solutions for the 3D Infrarelativistic Modelwith Radiation .............. 2236.1 Introduction............................................ 223<o:p></o:p>6.2 Reformation and Main Results.............................. 225<o:p></o:p>6.2.1 Reformation of Model............................... 225<o:p></o:p>6.2.2 Main Theorems.................................... 228<o:p></o:p>6.3 Global Existence and Asymptotic Behavior in H1 ................ 229<o:p></o:p>6.3.1 Global Existence in H1............................... 230<o:p></o:p>6.3.2 Asymptotic Behavior in H1........................... 256<o:p></o:p>6.4 Global Existence and Asymptotic Behavior in H2 ................ 257<o:p></o:p>6.4.1 Global Existence in H2............................... 257<o:p></o:p>6.4.2 Asymptotic Behavior in H2........................... 260<o:p></o:p>6.5 Global Existence and Asymptotic Behavior in H4 ................ 261<o:p></o:p>6.5.1 Global Existence in H4 ...............................261<o:p></o:p>6.5.2 Asymptotic Behavior in H4........................... 273<o:p></o:p>6.6 Bibliographic Comments................................... 276<o:p></o:p>Bibliography................................................. 277<o:p></o:p> Foreword................................................... IX<o:p></o:p>CHAPTER 1<o:p></o:p>Preliminary................................................. 1<o:p></o:p>1.1 Sobolev Spaces and Their Basic Properties..................... 1<o:p></o:p>1.1.1 Weak Derivatives and Their Properties.................. 1<o:p></o:p>1.1.2 Sobolev Spaces..................................... 4<o:p></o:p>1.1.3 Some Properties of Sobolev Spaces...................... 5<o:p></o:p>1.2 Some Inequalities in Analysis............................... 12<o:p></o:p>1.2.1 The Young Inequality................................ 12<o:p></o:p>1.2.2 The Poincaré Inequality.............................. 13<o:p></o:p>1.2.3 The Bellman–Gronwall Inequality...................... 13<o:p></o:p>1.2.4 The Hölder Inequality............................... 14<o:p></o:p>1.2.5 The Minkowski Inequality............................ 15<o:p></o:p>1.2.6 The Jensen Inequality............................... 15<o:p></o:p>1.2.7 The Shen–Zheng Inequality........................... 16<o:p></o:p>1.2.8 The Interpolation Inequality........................... 19<o:p></o:p>1.2.9 The Gagliardo–Nirenberg Interpolation Inequality .......... 19<o:p></o:p>1.3 C0-Semigroup........................................... 20<o:p></o:p>CHAPTER 2<o:p></o:p>Global Existence and Exponential Stability of Spherically Symetric Solutions to a Compressible CombustionRadiative and Reactive Gas ...... 232.1 Introduction............................................ 23<o:p></o:p>2.2 Model and Main Results................................... 24<o:p></o:p>2.2.1 Combustion Model of Radiative and Reactive Gas .......... 24<o:p></o:p>2.2.2 Spherical Symmetry Model of Combustion Model ........... 25<o:p></o:p>2.2.3 Main Theorems.................................... 28<o:p></o:p>2.3 Global Existence and Exponential Stability in H1 ................ 30<o:p></o:p>2.3.1 Global Existence of Solutions in H1..................... 31<o:p></o:p>2.3.2 Exponential Stability of Solutions in H1.................. 55<o:p></o:p>2.4 Global Existence and Exponential Stability in H2 ................ 67<o:p></o:p>2.4.1 Global Existence of Solutions in H2..................... 67<o:p></o:p>2.4.2 Exponential Stability of Solutions in H2.................. 74<o:p></o:p>2.5 Global Existence and Exponential Stability in H4 ................ 75<o:p></o:p>2.5.1 Global Existence of Solutions in H4..................... 75<o:p></o:p>2.5.2 Exponential Stability of Solutions in H4.................. 87<o:p></o:p>2.6 Bibliographic Comments................................... 90<o:p></o:p>CHAPTER 3<o:p></o:p>Global Existence, Uniqueness and Exponential Stability of Solutions<o:p></o:p>for the One-Dimensional Navier–Stokes Equations with Capillarity ........ 93<o:p></o:p>3.1 Introduction............................................ 93<o:p></o:p>3.2 Model and Main Results................................... 94<o:p></o:p>3.2.1 Korteweg-Type Model............................... 94<o:p></o:p>3.2.2 Main Theorems.................................... 97<o:p></o:p>3.3 Global Existence and Exponential Stability in H1 þ ............... 993.3.1 Global Existence in H1 þ .............................. 993.3.2 Asymptotic Behavior in H1 þ ........................... 1143.3.3 Exponential Stability in H1 þ ........................... 1203.4 Global Existence and Exponential Stabilityin H2 þ ............... 1223.4.1 Global Existence and Uniqueness in H2 þ .................. 1223.4.2 Exponential Stability in H2 þ ........................... 1253.5 Global Existence and Exponential Stabilityin H4 þ ............... 1263.5.1 Global Existence in H4 þ .............................. 1263.5.2 Asymptotic Behavior of Solutions in H4 þ ................. 1323.5.3 Exponential Stability in H4 þ ........................... 1343.6 Bibliographic Comments................................... 137<o:p></o:p>CHAPTER 4<o:p></o:p>Exponential Stability of Solutions for theCompressible p-th Power Newtonian Fluid with Large Initial Data........................... 1394.1 Introduction............................................ 139<o:p></o:p>4.2 Model and Main Results................................... 140<o:p></o:p>4.3 Global Existence and Exponential Stability in H1 ................ 143<o:p></o:p>4.3.1 Global Existence in H1 ...............................143<o:p></o:p>4.3.2 Exponential Stability in H1........................... 162<o:p></o:p>4.4 Global Existence and Exponential Stability in H2 ................ 163<o:p></o:p>4.5 Global Existence and Exponential Stability in H4 ................ 165<o:p></o:p>4.6 Bibliographic Comments................................... 166<o:p></o:p>CHAPTER 5<o:p></o:p>Global Existence and Asymptotic Behavior of Spherically Symmetric<o:p></o:p>Solutions for the Multi-Dimensional Infrarelativistic Model .............. 169<o:p></o:p>5.1 Introduction............................................ 169<o:p></o:p>5.2 Reformulation and Main Theorems........................... 171<o:p></o:p>5.2.1 Reformulation of Model.............................. 171<o:p></o:p>5.2.2 Main Theorems.................................... 174<o:p></o:p>5.3 Global Existence and Asymptotic Behavior in H1 ................ 177<o:p></o:p>5.3.1 Global Existence in H1............................... 177<o:p></o:p>5.3.2 Asymptotic Behavior in H1........................... 196<o:p></o:p>5.4 Global Existence and Asymptotic Behavior inH2 ................ 201<o:p></o:p>5.4.1 Global Existence in H2............................... 201<o:p></o:p>5.4.2 Asymptotic Behavior in H2........................... 205<o:p></o:p>5.5 Global Existence and Asymptotic Behavior in H4 ................ 206<o:p></o:p>5.5.1 Global Existence in H4............................... 206<o:p></o:p>5.5.2 Asymptotic Behavior in H4........................... 219<o:p></o:p>5.6 Bibliographic Comments................................... 221<o:p></o:p>CHAPTER 6<o:p></o:p>Global Existence and Asymptotic Behavior of Cylindrically Symmetric Solutions for the 3D Infrarelativistic Model with Radiation .............. 2236.1 Introduction............................................ 223<o:p></o:p>6.2 Reformation and Main Results.............................. 225<o:p></o:p>6.2.1 Reformation of Model............................... 225<o:p></o:p>6.2.2 Main Theorems.................................... 228<o:p></o:p>6.3 Global Existence and Asymptotic Behavior in H1 ................ 229<o:p></o:p>6.3.1 Global Existence in H1............................... 230<o:p></o:p>6.3.2 Asymptotic Behavior in H1........................... 256<o:p></o:p>6.4 Global Existence and Asymptotic Behavior inH2 ................ 257<o:p></o:p>6.4.1 Global Existence in H2............................... 257<o:p></o:p>6.4.2 Asymptotic Behavior in H2........................... 260<o:p></o:p>6.5 Global Existence and Asymptotic Behavior in H4 ................ 261<o:p></o:p>6.5.1 Global Existence in H4 ...............................261<o:p></o:p>6.5.2 Asymptotic Behavior in H4........................... 273<o:p></o:p>6.6 Bibliographic Comments................................... 276<o:p></o:p>Bibliography................................................. 277<o:p></o:p> 21 00 06 01 https://laboutique.edpsciences.fr/produit/1322/9782759829064/global-well-posedness-for-some-fluid-models 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/982/881/original/9782759829057-Global_Well-Posedness_couv-sofedis.jpg 17 14 20240913T181942+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20230216 01 00 20230216 19 00 20230216 2026 06 3052868830012 01 WORLD 13 03 9782759829057 15 9782759829057 WORLD 08 EDP Sciences & Science Press 04 01 00 20230216 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 61.99 01 5.50 3.23 EUR 04 06 01 02 1 00 217.99 01 5.50 3.23 EUR 01 04 06 01 02 1 00 238.99 01 5.50 12.46 USD 01