On the uniqueness in critical spaces for compressible Navier-Stokes equations

被引：67

作者：

Danchin, R ^{[1
]}

机构：

[1] Univ Paris 12, Lab Anal Math Appl, F-94010 Creteil, France

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2005年 / 12卷 / 01期

关键词：

compressible fluids; Navier-Stokes equations; uniqueness; critical regularity; logarithmic interpolation;

D O I：

10.1007/s00030-004-2032-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show some new uniqueness results for compressible flows with data having critical regularity. In the barotropic case, uniqueness is stated whenever the space dimension N satisfies N >= 2, and in the polytropic case, whenever N >= 3. The endpoints N = 2 in the barotropic case and N = 3 in the polytropic case were left open in [4], [5] and [6].

引用

页码：111 / 128

页数：18

共 14 条

[1]

[Anonymous], 1980, J MATH KYOTO U

[2] Quasilinear wave equations and Strichartz estimations [J].

Bahouri, H ;

Chemin, JY .

AMERICAN JOURNAL OF MATHEMATICS, 1999, 121 (06) :1337-1377

[3] FLOW OF NON-LIPSCHITZ VECTOR-FIELDS AND NAVIER-STOKES EQUATIONS [J].

CHEMIN, JY ;

LERNER, N .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 121 (02) :314-328

[4]

Chemin JY, 1999, J ANAL MATH, V77, P27, DOI 10.1007/BF02791256

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

Danchin, R .

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

[6] Density-dependent incompressible viscous fluids in critical spaces [J].

Danchin, R .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 :1311-1334

[7] 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

[8] Local theory in critical spaces for compressible viscous and heat-conductive gases [J].

Danchin, R .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2001, 26 (7-8) :1183-1233

[9]

Danchin R., 2001, Differ. Integral Equ, V14, P953

[10] ON THE NAVIER-STOKES INITIAL VALUE PROBLEM .1. [J].

FUJITA, H ;

KATO, T .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1964, 16 (04) :269-315

← 1 2 →