Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916364123373568 |
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| author | Goodair, Daniel |
| author_facet | Goodair, Daniel |
| contents | We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs Goodair, Daniel Analysis of PDEs Probability We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence. |
| title | Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2408.11678 |