A survey with new extensions of the maximal-regularity framework for nonlinear SPDEs, yielding local well-posedness, blow-up criteria, and instantaneous regularization in critical spaces.
Surface quasi-geostrophic equations forced by random noise: prescribed energy and non-unique Markov selections
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abstract
We consider the momentum formulation of the two-dimensional surface quasi-geostrophic equations forced by random noise, of both additive and linear multiplicative types. For any prescribed deterministic function under some conditions, we construct solutions to each system whose energy is the fixed function. Consequently, we prove non-uniqueness of almost sure Markov selections of suitable class of weak solutions associated to the momentum surface quasi-geostrophic equations in both cases of noise.
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Nonlinear SPDEs and Maximal Regularity: An Extended Survey
A survey with new extensions of the maximal-regularity framework for nonlinear SPDEs, yielding local well-posedness, blow-up criteria, and instantaneous regularization in critical spaces.