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Surface quasi-geostrophic equations forced by random noise: prescribed energy and non-unique Markov selections

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arxiv 2407.00920 v1 pith:36223J7B submitted 2024-07-01 math.AP math.PR

Elliott Walker , Kazuo Yamazaki This is my paper · ORCID
classification math.APmath.PR
keywords equationsnoisequasi-geostrophicsurfaceenergyforcedfunctionmarkov
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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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Cited by 1 Pith paper

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  1. Nonlinear SPDEs and Maximal Regularity: An Extended Survey

    math.PR 2025-01 conditional novelty 4.0 of 10

    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.

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