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Quasilinear parabolic stochastic evolution equations via maximal Lp-regularity

Hornung, Luca

Abstract:
We study the Cauchy problem for an abstract quasilinear stochastic parabolic evolution equation on a Banach space driven by a cylindrical Brownian motion. We prove existence and uniqueness of a local strong solution up to a maximal stopping time, that is characterised by a blow-up alternative. The key idea is an iterative application of the theory about maximal Lp- regularity for semilinear stochastic evolution equations by Van Neerven, Veraar and Weis. We apply our local well-posedness result to a convection-diffusion equation on a bounded domainwith Dirichlet,Neumann ormixed boudary conditions and to a generalizedNavier-Stokes equation describing non-Newtonian fluids. In the first example, we can even show that the solution exists globally.

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Volltext §
DOI: 10.5445/IR/1000062621
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-626216
KITopen-ID: 1000062621
Verlag KIT, Karlsruhe
Umfang 47 S.
Serie CRC 1173 ; 2016/34
Schlagworte quasilinear stochastic equations, maximal regularity, blow-up behavior, stochastic convection-diffusion equation, functional calculus
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