SPDE in Hilbert space with locally monotone coefficients |
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Authors: | Wei Liu,Michael Rö ckner |
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Affiliation: | a Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany b Department of Mathematics and Statistics, Purdue University, West Lafayette, IN 47906, USA |
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Abstract: | The aim of this paper is to extend the usual framework of SPDE with monotone coefficients to include a large class of cases with merely locally monotone coefficients. This new framework is conceptually not more involved than the classical one, but includes many more fundamental examples not included previously. Thus our main result can be applied to various types of SPDEs such as stochastic reaction-diffusion equations, stochastic Burgers type equation, stochastic 2-D Navier-Stokes equation, stochastic p-Laplace equation and stochastic porous media equation with non-monotone perturbations. |
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Keywords: | Stochastic evolution equation Locally monotone Coercivity Navier-Stokes equation Variational approach |
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