Abstract: Stochastic partial differential equations such as reaction-diffusion equations, nerve equations, the Navier Stokes equations or the primitive equation of the ocean, driven by white or coloured noise, play a prominent role in science and technology. We discuss a class of stochastic
evolution equations on L
p-spaces which offer a common framework for these equations and present
a spectral theoretic method which allows to reduce existence and regularity results for their solutions to estimates for basic ordinary stochastic differential equations. The L
p- setting is crucial for
handling rougher initial values and for obtaining better regularity results needed in computational
approaches to these equations.
