Sharp Inviscid Limit Results under Navier Type Boundary Conditions. An Lp Theory

被引：112

作者：

da Veiga, H. Beirao ^{[1
]}

Crispo, F. ^{[1
]}

机构：

[1] Univ Pisa, Dipartimento Matemat Applicata U Dini, I-56127 Pisa, Italy

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2010年 / 12卷 / 03期

关键词：

Navier-Stokes equations; inviscid limit; slip boundary conditions; VANISHING VISCOSITY LIMIT; STOKES EQUATIONS; INCOMPRESSIBLE FLUID; EULER EQUATIONS; WELL-POSEDNESS; PERTURBATION-THEORY; FLOW; EXISTENCE; REGULARITY; UNIQUENESS;

D O I：

10.1007/s00021-009-0295-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the evolutionary Navier-Stokes equations with a Navier slip-type boundary condition, and study the convergence of the solutions, as the viscosity goes to zero, to the solution of the Euler equations under the zero-flux boundary condition. We obtain quite sharp results in the 2-D and 3-D cases. However, in the 3-D case, we need to assume that the boundary is flat.

引用

页码：397 / 411

页数：15

共 41 条

[1]

[Anonymous], SPRINGER TRACTS NATU

[2]

[Anonymous], 1969, QUELQUES METHODES RE

[3] Regularity for the Navier-Stokes equations with slip boundary condition [J].

Bae, Hyeong-Ohk ;

Jin, Bum Ja .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (07) :2439-2443

[4] EXISTENCE AND UNIQUENESS OF SOLUTION TO BIDIMENSIONAL EULER EQUATION [J].

BARDOS, C .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 40 (03) :769-790

[5]

BEGUE C, 1988, PITMAN RES NOTES MAT, V181

[6]

Beirao da Veiga H., 2007, Port. Math. (N.S.), V64, P377

[7]

BOURGUIGNON J. P., 1931, J. Funct. Anal., V15, P341, DOI [10.1016/0022-1236(74)90027-5, DOI 10.1016/0022-1236(74)90027-5]

[8] On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions [J].

Clopeau, T ;

Mikelic, A ;

Robert, R .

NONLINEARITY, 1998, 11 (06) :1625-1636

[9]

Constantin P, 1996, INDIANA U MATH J, V45, P67

[10] INVISCID LIMIT FOR VORTEX PATCHES [J].

CONSTANTIN, P ;

WU, JH .

NONLINEARITY, 1995, 8 (05) :735-742

← 1 2 3 4 5 →