The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit

Abstract

Well-posedness is proved for the stochastic viscous Cahn-Hilliard equation with homogeneous Neumann boundary conditions and Wiener multiplicative noise. The double-well potential is allowed to have any growth at infinity (in particular, also super-polynomial) provided that it is everywhere defined on the real line. A vanishing viscosity argument is carried out and the convergence of the solutions to the ones of the pure Cahn-Hilliard equation is shown. Some refined regularity results are also deduced for both the viscous and the non-viscous case.

arXiv commentKey words and phrases: stochastic viscous Cahn-Hilliard equation, singular potential, well-posedness, regularity, vanishing viscosity, variational approach

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• An extended variational theory for nonlinear evolution equations via modular spaces
• The stochastic Cahn-Hilliard equation with degenerate mobility and logarithmic potential