Smooth Solutions of Non-linear Stochastic Partial Differential Equations

Details Smooth Solutions of Non-linear Stochastic Partial Differential Equations Smooth Solutions of Non-linear Stochastic Partial Differential Equations

2008-01-25

arxiv.org/abs/0801.3883v1

Mathematics

Probability

26Pages

Scientific paper

In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau's equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes equation in the whole space, and obtain the existence of their respectively smooth solutions.

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