Regular solutions to the Navier-Stokes equations with an initial data in L(3, ∞)

被引：0

作者：

Maremonti, P. ^{[1
]}

机构：

[1] Seconda Univ Napoli, Dipartimento Matemat & Fis, Via Vivaldi 43, I-81100 Caserta, Italy

来源：

RICERCHE DI MATEMATICA | 2017年 / 66卷 / 01期

关键词：

Navier-Stokes equations; Existence and uniqueness; Global solutions; EXTERIOR DOMAINS; VISCOUS-FLUID; STABILITY; SPACE; MOVEMENT; FLOWS; DECAY;

D O I：

10.1007/s11587-016-0287-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Navier-Stokes initial boundary value problem in exterior domains Omega subset of R-n, n >= 3. We assume that the initial data belongs to L(n, infinity) suitable subspace of L(n, infinity) Lorentz space. We are able to prove on an interval (0, T) the existence of a unique regular solution, global in time for small data. The solution enjoys some new estimates and a new approach to the proof is exhibited.

引用

页码：65 / 97

页数：33

共 32 条

[1]

Alvino A., 1977, B UNIONE MAT ITAL, V14, P148

[2]

Bennett C., 1988, Interpolation of operators

[3] ON STABILITY OF EXTERIOR STATIONARY NAVIER-STOKES FLOWS [J].

BORCHERS, W ;

MIYAKAWA, T .

ACTA MATHEMATICA, 1995, 174 (02) :311-382

[4] Strong solutions to the incompressible Navier-Stokes equations in the half-space [J].

Cannone, M ;

Planchon, F ;

Schonbek, M .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (5-6) :903-924

[5]

Crispo F, 2004, REND SEMIN MAT U PAD, V112, P11

[6]

Foias C., 1961, Bull. Soc. Math. Fr., V89, P1

[7]

GALDI GP, 1978, RIC MAT, V27, P387

[8]

Galdi GP., 1994, An Introduction to the Mathematical Theory of the Navier-Stokes Equations

[9] ABSTRACT LP ESTIMATES FOR THE CAUCHY-PROBLEM WITH APPLICATIONS TO THE NAVIER-STOKES EQUATIONS IN EXTERIOR DOMAINS [J].

GIGA, Y ;

SOHR, H .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 102 (01) :72-94

[10] SOLUTIONS IN LR OF THE NAVIER-STOKES INITIAL-VALUE PROBLEM [J].

GIGA, Y ;

MIYAKAWA, T .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1985, 89 (03) :267-281

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