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

Arrieta, José; Carvalho, Alexandre

doi:10.1090/S0002-9947-99-02528-3

Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations
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by José M. Arrieta and Alexandre N. Carvalho PDF

Trans. Amer. Math. Soc. 352 (2000), 285-310 Request permission

Abstract:

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

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