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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.17668 |
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| _version_ | 1866909089263517696 |
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| author | Hausenblas, Erika Moghomye, Boris Jidjou |
| author_facet | Hausenblas, Erika Moghomye, Boris Jidjou |
| contents | The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differential equations. The idea is first to split the system by rewriting the non-linear part in a linear part acting on a given process $ξ$. This is done in such a way that the fixpoint with respect to $ξ$ would be the solution. However, to show the well posedness of the {\sl linearized} system, one needs a cut-off argument. Under which conditions one can handle the limits of the cut-off parameter to get in the end a martingale solution of the original system is given in the Meta-Theorem.
Secondly, we want to verify the full applicability of the Meta Theorem by showing the existence of a martingale solution of a highly nonlinear chemotaxis system with underlying fluid dynamic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Meta Theorem for nonlinear stochastic coupled systems: Application to stochastic chemotaxis-Stokes porous media Hausenblas, Erika Moghomye, Boris Jidjou Probability The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differential equations. The idea is first to split the system by rewriting the non-linear part in a linear part acting on a given process $ξ$. This is done in such a way that the fixpoint with respect to $ξ$ would be the solution. However, to show the well posedness of the {\sl linearized} system, one needs a cut-off argument. Under which conditions one can handle the limits of the cut-off parameter to get in the end a martingale solution of the original system is given in the Meta-Theorem. Secondly, we want to verify the full applicability of the Meta Theorem by showing the existence of a martingale solution of a highly nonlinear chemotaxis system with underlying fluid dynamic. |
| title | A Meta Theorem for nonlinear stochastic coupled systems: Application to stochastic chemotaxis-Stokes porous media |
| topic | Probability |
| url | https://arxiv.org/abs/2401.17668 |