Well-posedness of stochastic partial differential equations with fully local monotone coefficients
The authors establish the wellposedness for stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple which play significant roles in modeling the real world evolution process, such as fluid dynamics, etc. The diffusion coefficient may depend on the gradient of the solution. The authors innovatively combine the pseudo-monotonicity techniques and compactness arguments to obtain the results. This work solves a longstanding open problem and make great progress in this field.
stochastic partial differential equations
scientific article; zbMATH DE number 7932384
scientific article