On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations
| Autor: | Rongchan Zhu, Martina Hofmanová, Xiangchan Zhu |
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| Rok vydání: | 2021 |
| Předmět: |
Class (set theory)
Markov chain Applied Mathematics General Mathematics Probability (math.PR) Euler equations symbols.namesake Mathematics - Analysis of PDEs Stopping time FOS: Mathematics Dissipative system symbols Applied mathematics Uniqueness Martingale (probability theory) Mathematics - Probability Well posedness Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Communications on Pure and Applied Mathematics |
| ISSN: | 0010-3640 |
| DOI: | 10.1002/cpa.22023 |
| Popis: | We are concerned with the question of well-posedness of stochastic, three-dimensional, incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak-strong uniqueness; (iii) nonuniqueness in law; (iv) existence of a strong Markov solution; (v) nonuniqueness of strong Markov solutions: all hold true within this class. Moreover, as a by-product of (iii) we obtain existence and nonuniqueness of probabilistically strong and analytically weak solutions defined up to a stopping time and satisfying an energy inequality. (c) 2021 Wiley Periodicals LLC. |
| Databáze: | OpenAIRE |
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