Solutions to the stochastic thin-film equation for initial values with non-full support
| Autor: | Dareiotis, Konstantinos, Gess, Benjamin, Gnann, Manuel V., Sauerbrey, Max |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\alpha$-entropy dissipation and the conservation of mass. Comment: Accepted for publication in Transactions of the AMS. Minor corrections. 36 pages |
| Databáze: | arXiv |
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