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

Authors
Arrieta, JM Carvalho, AN
Citation
Jm. Arrieta et An. Carvalho, Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations, T AM MATH S, 352(1), 2000, pp. 285-310
Citations number
19
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
352
Issue
1
Year of publication
2000
Pages
285 - 310
Database
ISI
SICI code
0002-9947(200001)352:1<285:APPWCN>2.0.ZU;2-S
Abstract
We prove a local existence and uniqueness theorem for abstract parabolic pr oblems of the type (x)over dot = Ax+f(t,x) when the nonlinearity f satisfie s certain critical conditions. We apply this abstract result to the Navier- Stokes and heat equations.