Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations

By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path depen...

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Published inPotential analysis Vol. 61; no. 2; pp. 379 - 407
Main Authors Ren, Panpan, Tang, Hao, Wang, Feng-Yu
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2024
Springer Nature B.V
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ISSN0926-2601
1572-929X
DOI10.1007/s11118-023-10113-5

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Summary:By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path dependent stochastic transport type equations, which are arising from stochastic fluid mechanics with forces depending on the history and the environment. In particular, the distribution-path dependent stochastic Camassa-Holm equation with or without Coriolis effect has a unique global solution when the noise is strong enough, whereas for the deterministic model wave-breaking may occur. This indicates that the noise may prevent blow-up almost surely.
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ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-023-10113-5