Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations

被引：112

作者：

Arrieta, JM ^{[1
]}

Carvalho, AN

机构：

[1] Univ Complutense Madrid, Fac Matemat, Dept Matemat Aplicada, E-28040 Madrid, Spain

[2] Univ Sao Paulo, Inst Ciencias Matemat Sao Carlos, Dept Matemat, Sao Carlos, SP, Brazil

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 352卷 / 01期

关键词：

abstract parabolic equations; critical nonlinearities; growth conditions; local existence; uniqueness; Navier-Stokes; heat equations;

D O I：

10.1090/S0002-9947-99-02528-3

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

We prove a local existence and uniqueness theorem for abstract parabolic problems of the type (x)over dot = Ax+f(t,x) when the nonlinearity f satisfies certain critical conditions. We apply this abstract result to the Navier-Stokes and heat equations.

引用

页码：285 / 310

页数：26

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