Stationary Solutions to the Stochastic Burgers Equation on the Line
| Autor: | Cole Graham, Lenya Ryzhik, Alexander Dunlap |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Function space Probability (math.PR) 010102 general mathematics FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) 60H15 35R60 Space (mathematics) 01 natural sciences Burgers' equation Periodic function Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics Convex combination 010307 mathematical physics Invariant measure 0101 mathematics Invariant (mathematics) Indecomposable module Mathematics - Probability Mathematical Physics Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Communications in Mathematical Physics. 382:875-949 |
| ISSN: | 1432-0916 0010-3616 |
| Popis: | We consider invariant measures for the stochastic Burgers equation on $\mathbb{R}$, forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in space. An invariant measure is indecomposable, or extremal, if it cannot be represented as a convex combination of other invariant measures. We show that for each $a\in\mathbb{R}$, there is a unique indecomposable law of a spacetime-stationary solution with mean $a$, in a suitable function space. We also show that solutions starting from spatially-decaying perturbations of mean-$a$ periodic functions converge in law to the extremal space-time stationary solution with mean $a$ as time goes to infinity. 68 pages, to appear in Communications in Mathematical Physics |
| Databáze: | OpenAIRE |
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