GLOBAL LARGE SOLUTIONS TO THE THREE DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS

被引：17

作者：

Zhai, Xiaoping ^{[1
]}

Li, Yongsheng ^{[2
]}

Zhou, Fujun ^{[2
]}

机构：

[1] Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China

[2] South China Univ Technol, Sch Math, Guangzhou 510640, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2020年 / 52卷 / 02期

基金：

中国国家自然科学基金;

关键词：

compressible Navier-Stokes equations; global large solutions; Littlewood-Paley theory; weighted Chemin-Lerner technique; WELL-POSEDNESS; CRITICAL SPACES; STABILITY; EXISTENCE; LIMIT; FLOW;

D O I：

10.1137/19M1265843

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the global large solutions to the 3 dimensional compressible Navier-Stokes equations in the critical Besov spaces with initial data satisfying a nonlinear smallness condition. Here the "large solutions" mean that the any component of the initial velocity could be arbitrarily large. Moreover, we give an example of initial data satisfying the nonlinear smallness condition, while the norms of each component are arbitrarily large. Our approach is inspired by the weighted Chemin-Lerner technique used for the incompressible Navier-Stokes equations.

引用

页码：1806 / 1843

页数：38

共 50 条

[1] LARGE GLOBAL SOLUTIONS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN THREE DIMENSIONS
Zhai, Xiaoping
Chen, Yiren
LI, Yongsheng
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2023, 43 (01): : 309 - 337
[2] Global large solutions to the two-dimensional compressible Navier-Stokes equations
Zhai, Xiaoping
Chen, Zhi-Min
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (02):
[3] Global Large Solutions and Incompressible Limit for the Compressible Navier-Stokes Equations
Chen, Zhi-Min
Zhai, Xiaoping
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2019, 21 (02)
[4] GLOBAL EXISTENCE OF MARTINGALE SOLUTIONS TO THE THREE-DIMENSIONAL STOCHASTIC COMPRESSIBLE NAVIER-STOKES EQUATIONS
Wang, Dehua
Wang, Huaqiao
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2015, 28 (11-12) : 1105 - 1154
[5] GLOBAL WEAK SOLUTIONS FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS
SERRE, D
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1986, 303 (13): : 639 - 642
[6] Global solutions of the compressible Navier-Stokes equations with large discontinuous initial data
Chen, GQ
Hoff, D
Trivisa, K
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (11-12) : 2233 - 2257
[7] Global attractors for the Navier-Stokes equations of three-dimensional compressible flow
Feireisl, E
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (01): : 35 - 39
[8] ON THE STABILITY OF GLOBAL SOLUTIONS TO THE THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS
Bahouri, Hajer
Chemin, Jean-Yves
Gallagher, Isabelle
[J]. JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES, 2018, 5 : 843 - 911
[9] On global solutions of Cauchy problems for compressible Navier-Stokes equations
Kawashita, M
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 48 (08) : 1087 - 1105
[10] Global solutions of the Navier-Stokes equations for viscous compressible flows
Wang, DH
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (08) : 1867 - 1890

← 1 2 3 4 5 →