The initial value problem for the compressible Navier-Stokes equations without heat conductivity

被引：7

作者：

Chen, Qing ^{[1
]}

Tan, Zhong ^{[2
]}

Wu, Guochun ^{[3
]}

Zou, Weiyuan ^{[4
]}

机构：

[1] Xiamen Univ Technol, Sch Appl Math, Xiamen 361024, Fujian, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[3] Huaqiao Univ, Fujian Prov Univ Key Lab Computat Sci, Sch Math Sci, Quanzhou 362021, Peoples R China

[4] Beijing Univ Chem Technol, Coll Math & Phys, Beijing 100029, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equations; Global existence; Optimal convergence rates; BOUNDARY-VALUE-PROBLEMS; LARGE-TIME BEHAVIOR; GLOBAL EXISTENCE; CONVERGENCE-RATES; CRITICAL SPACES; WEAK SOLUTIONS; DECAY; MOTION; FLOWS; SYSTEMS;

D O I：

10.1016/j.jde.2019.11.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are concerned with the global existence and convergence rates of strong solutions for the compressible Navier-Stokes equations without heat conductivity in R-3. The global existence and uniqueness of strong solutions are established by the delicate energy method under the condition that the initial data are close to the constant equilibrium state in H-2-framework. Furthermore, if additionally the initial data belong to L-1, the optimal convergence rates of the solutions in L-2-norm and convergence rates of their spatial derivatives in L-2-norm are obtained. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：5469 / 5490

页数：22

共 43 条

[1] A Global Existence Result for the Compressible Navier-Stokes Equations in the Critical Lp Framework [J].

Charve, Frederic ;

Danchin, Raphael .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 198 (01) :233-271

[2] Global existence in critical spaces for compressible Navier-Stokes equations [J].

Danchin, R .

INVENTIONES MATHEMATICAE, 2000, 141 (03) :579-614

[3] Global existence in critical spaces for flows of compressible viscous and heat-conductive gases [J].

Danchin, R .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 160 (01) :1-39

[4]

Danchin R., 2005, LECT NOTES, V14

[5] DECAY-ESTIMATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN UNBOUNDED-DOMAINS [J].

DECKELNICK, K .

MATHEMATISCHE ZEITSCHRIFT, 1992, 209 (01) :115-130

[6] Optimal convergence rates for the compressible Navier-Stokes equations with potential forces [J].

Duan, Renjun ;

Ukai, Seiji ;

Yang, Tong ;

Zhao, Huijiang .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2007, 17 (05) :737-758

[7] Optimal Lp-Lq convergence rates for the compressible Navier-Stokes equations with potential force [J].

Duan, Renjun ;

Liu, Hongxia ;

Ukai, Seiji ;

Yang, Tong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 238 (01) :220-233

[8] Global Existence and Convergence Rates for the 3-D Compressible Navier-Stokes Equations without Heat Conductivity [J].

Duan, Renjun ;

Ma, Hongfang .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (05) :2299-2319

[9]

Evans L.C., 1998, PARTIAL DIFFERENTIAL

[10] A blow-up criterion for compressible viscous heat-conductive flows [J].

Fan, Jishan ;

Jiang, Song ;

Ou, Yaobin .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (01) :337-350

← 1 2 3 4 5 →