GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

doi:10.1016/S0252-9602(12)60166-0

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (6): 2141-2160.doi: 10.1016/S0252-9602(12)60166-0

GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

张培欣^1,2|邓雪梅³|赵俊宁¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China；
2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China；
3. College of Science, China Three Gorges University, Yichang 443002, China

收稿日期:2011-07-04 出版日期:2012-11-20 发布日期:2012-11-20
基金资助:
This work was partially supported by National Natural Science Foundation of China (11001090) and the Fundamental Research Funds for the Central Universities (11QZR16).

GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

ZHANG Pei-Xin^1,2, DENG Xue-Mei³, ZHAO Jun-Ning¹

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China；
2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China；
3. College of Science, China Three Gorges University, Yichang 443002, China

Received:2011-07-04 Online:2012-11-20 Published:2012-11-20
Supported by:
This work was partially supported by National Natural Science Foundation of China (11001090) and the Fundamental Research Funds for the Central Universities (11QZR16).

摘要/Abstract

摘要：

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ||ρ0||_L∞ is appropriate small and 1 << 6/ 5 . Here the initial density could have vacuum and we do not require that the initial energy is small.

关键词: compressible Navier-Stokes equations, global classical solutions, general ini-tial energy

Abstract:

Key words: compressible Navier-Stokes equations, global classical solutions, general ini-tial energy

中图分类号:

76N10

张培欣, 邓雪梅, 赵俊宁. GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY[J]. 数学物理学报(英文版), 2012, 32(6): 2141-2160.

ZHANG Pei-Xin, DENG Xue-Mei, ZHAO Jun-Ning. GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2141-2160.

参考文献

[1] Hoff D. Global existence for 1D, compressible, isentropic Navier-Stokes equations with large initial data. Trans Amer Math Soc, 1987, 303(1): 169–181

[2] Kazhikov A V, Shelukhin V V. Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas. Prikl Mat Meh, 1977, 41: 282–291

[3] Serre D. Solutions faibles globales des ´equations de Navier-Stokes pour un fluide compressible. C R Acad Sci Paris S´er I Math, 1986, 303: 639–642

[4] Serre D. 1´équation monodimensionnelle d´un fluide visqueux, compressible et conducteur de chaleur. C R Acad Sci Paris S´er I Math, 1986, 303: 703–706

[5] Nash J. Le problème de Cauchy pour les équations diff´erentielles d´un fluide g´en´eral. Bull Soc Math France, 1962, 90: 487–497

[6] Serrin J. On the uniqueness of compressible fluid motion. Arch Rational Mech Anal, 1959, 3: 271–288

[7] Cho Y, Choe H J, Kim H. Unique solvability of the initial boundary value problems for compressible viscous fluid. J Math Pures Appl, 2004, 83: 243–275

[8] Cho Y, Kim H. On classical solutions of the compressible Navier-Stokes equations with nonnegative intial densities. Manuscript Math, 2006, 120: 91–129

[9] Cho Y, Kim H. Strong solutions of the Navier-Stokes equations for isentropic compressible fluids. J Differ Eqs, 2003, 190: 504–523

[10] Salvi R, Straskraba I. Global existence for viscous compressible fluids and their behavior as t ! 1. J Fac Sci Univ Tokyo Sect IA Math, 1993, 40: 17–51

[11] Matsumura A, Nishida T. The initial value problem for the equations of motion of viscous and heat-conductive gases. J Math Kyoto Univ, 1980, 20(1): 67–104

[12] Hoff D. Global solutions of the Navier-Stokes equations for multidimendional compressible flow with dis-constinuous initial data. J Differ Eqs, 1995, 120(1): 215–254

[13] Hoff D. Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations fo state and discontinuous initial data. Arch Rational Mech Anal, 1995, 132: 1–14

[14] Lions P L. Mathematical Topics in Fluid Mechanics. Vol 2. Compressible Models. New York: Oxford University Press, 1998

[15] Feiresl E, Novotny A, Petzeltov´a H. On the existence of globally defined weak solutions to the Navier-Stokes equations. J Math Fluid Mech, 2001, 3(4): 358–392

[16] Zhang T, Fang D Y. Compressible flows with a density-dependent viscosity coefficient. SIAM J Math Anal, 2010, 41(6): 2453–2488

[17] Zhang T. Global solutions of compressible barotropic Navier-Stokes equations with a density-dependent viscosity coefficient. J Math Phys, 2011, 52(4): 043510

[18] Huang X D, Li J, Xin Z P. Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations. Comm Pure Appl Math, 2012, 65(4): 549–585

[19] Deng X M, Zhang P X, Zhao J N. Global Well-posedness of Classical Solutions with Large Initial data and Vacuum to the Three-dimensional isentropic compressible Navier-Stokes equations. Preprint

[20] Beal J T, Kato T, Majda A. Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun Math Phys, 1984, 94: 61–66

GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

Metrics

本文评价

推荐阅读 0

[1]	黄飞敏, 王勇. MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION[J]. 数学物理学报(英文版), 2018, 38(5): 1549-1566.
[2]	唐少君, 张澜. NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION[J]. 数学物理学报(英文版), 2018, 38(3): 973-1000.
[3]	Hakho HONG, 王腾. ZERO DISSIPATION LIMIT TO A RIEMANN SOLUTION FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS[J]. 数学物理学报(英文版), 2017, 37(5): 1177-1208.
[4]	叶嵎林. GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2016, 36(5): 1419-1432.
[5]	孔慧慧, 李海梁, 张兴伟. A BLOW-UP CRITERION OF SPHERICALLY SYMMETRIC STRONG SOLUTIONS TO 3D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2016, 36(4): 1153-1166.
[6]	何躏, 唐少君, 王涛. STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY[J]. 数学物理学报(英文版), 2016, 36(1): 34-48.
[7]	Hakho Hong, Feimin Huang. ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2012, 32(1): 389-412.
[8]	江松, 欧耀彬. A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS[J]. 数学物理学报(英文版), 2010, 30(6): 1851-1864.