On Kato's Method for Navier-Stokes Equations

被引：10

作者：

Haak, Bernhard H. ^{[1
]}

Kunstmann, Peer Chr. ^{[2
]}

机构：

[1] Inst Math Bordeaux, F-33405 Talence, France

[2] Univ Karlsruhe, Int Anal, D-76128 Karlsruhe, Germany

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2009年 / 11卷 / 04期

关键词：

Mild solutions; Navier-Stokes equations; Kato's method; parabolic equations; quadratic non-linearity; admissibility of unbounded operators; FOURIER MULTIPLIER THEOREMS; FRACTIONAL INTEGRALS; INTERPOLATION; PERTURBATION; REGULARITY; OPERATORS;

D O I：

10.1007/s00021-008-0270-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate Kato's method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier-Stokes equations, our approach unifies several results known in the literature, partly with different proofs. Moreover, we establish new existence and uniqueness results for rough initial data on arbitrary domains in R-3 and irregular domains in R-n.

引用

页码：492 / 535

页数：44

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