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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.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000062621
ISSN: 2365-662X
URN: 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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