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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| Veröffentlicht in: | Potential analysis 2024, Vol.61 (2), p.379-407 |
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| container_title | Potential analysis |
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| creator | Ren, Panpan Tang, Hao Wang, Feng-Yu |
| description | 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. |
| doi_str_mv | 10.1007/s11118-023-10113-5 |
| format | Article |
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| subjects | Coriolis effect Fluid dynamics Fluid mechanics Functional Analysis Geometry Mathematics Mathematics and Statistics Partial differential equations Potential Theory Probability Theory and Stochastic Processes Uniqueness Wave breaking |
| title | Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations |
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