Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations. (English) Zbl 0785.34044

Rankin, Samuel M. III

Trans. Am. Math. Soc. 336, No. 2, 523-535 (1993).

The author proposes a rather complicated abstract semigroup-based theory for a class of semilinear evolution equations; next this theory is applied to a class of parabolic problems and to the Navier-Stokes equation. He does not seem to be aware of earlier results in the field which employ similar techniques in a simpler setup and with better results. A good reference is the article of Y. Giga and T. Miyakawa [Arch. Ration. Mech. Anal. 89, 267-281 (1985; Zbl 0587.35078)].

Reviewer: D.Tătaru (Evaston)

MSC:

34G20	Nonlinear differential equations in abstract spaces
35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations
35Q30	Navier-Stokes equations

Keywords:

semigroups; semilinear evolution equations; parabolic problems; Navier- Stokes equation

Citations:

Zbl 0587.35078