Solutions to the stochastic thin-film equation for initial values with non-full support
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866913568608223232 |
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| author | Dareiotis, Konstantinos Gess, Benjamin Gnann, Manuel V. Sauerbrey, Max |
| author_facet | Dareiotis, Konstantinos Gess, Benjamin Gnann, Manuel V. Sauerbrey, Max |
| contents | The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on existing results in three aspects: (1) Non-quadratic mobility with not necessarily strictly positive initial data, (2) Measure-valued initial data, (3) Less spatial regularity of the noise. This is achieved by carrying out a compactness argument based solely on the control of the $α$-entropy dissipation and the conservation of mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solutions to the stochastic thin-film equation for initial values with non-full support Dareiotis, Konstantinos Gess, Benjamin Gnann, Manuel V. Sauerbrey, Max Analysis of PDEs Probability 35R60, 76A20 The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on existing results in three aspects: (1) Non-quadratic mobility with not necessarily strictly positive initial data, (2) Measure-valued initial data, (3) Less spatial regularity of the noise. This is achieved by carrying out a compactness argument based solely on the control of the $α$-entropy dissipation and the conservation of mass. |
| title | Solutions to the stochastic thin-film equation for initial values with non-full support |
| topic | Analysis of PDEs Probability 35R60, 76A20 |
| url | https://arxiv.org/abs/2305.06017 |