Existence, uniqueness and regularity for the stochastic Ericksen-Leslie equation
| Autor: | Anne de Bouard, Antoine Hocquet, Andreas Prohl |
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| Přispěvatelé: | Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut für Mathematik [Berlin], Technische Universität Berlin (TU), Mathematisches Institut [Tübingen], Eberhard Karls Universität Tübingen = Eberhard Karls University of Tuebingen |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Class (set theory)
Pure mathematics stochastic partial differential equations 60H15 76A15 35K55 58E20 General Physics and Astronomy 01 natural sciences liquid crystals Mathematics - Analysis of PDEs Critical space FOS: Mathematics harmonic maps Mathematics Subject Classification -60H15 Uniqueness [MATH]Mathematics [math] 0101 mathematics Mathematical Physics Mathematics 58E20 Applied Mathematics Probability (math.PR) non-linear parabolic equations 010102 general mathematics Probabilistic logic Statistical and Nonlinear Physics Torus 010101 applied mathematics Compact space 76A15 Flow (mathematics) Colors of noise 35K55 Mathematics - Probability Analysis of PDEs (math.AP) |
| Zdroj: | Nonlinearity Nonlinearity, IOP Publishing, In press, ⟨10.1088/1361-6544/ac022e⟩ |
| ISSN: | 0951-7715 1361-6544 |
| DOI: | 10.1088/1361-6544/ac022e⟩ |
| Popis: | We investigate existence and uniqueness for the stochastic liquid crystal flow driven by colored noise on the two-dimensional torus. After giving a natural uniqueness criterion, we prove local solvability in $L^p$-based spaces, for every $p>2.$ Thanks to a bootstrap principle together with a Gy��ngy-Krylov-type compactness argument, this will ultimately lead us to prove the existence of a particular class of global solutions which are partially regular, strong in the probabilistic sense, and taking values in the "critical space" $L^2\times H^1.$ 53 pages |
| Databáze: | OpenAIRE |
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