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 in | Potential analysis Vol. 61; no. 2; pp. 379 - 407 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
01.08.2024
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
ISSN | 0926-2601 1572-929X |
DOI | 10.1007/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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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
ISSN: | 0926-2601 1572-929X |
DOI: | 10.1007/s11118-023-10113-5 |