EXISTENCE, UNIQUENESS AND REGULARITY FOR THE STOCHASTIC ERICKSEN-LESLIE EQUATION

Anne de Bouard (1) , Antoine Hocquet (2) , Andreas Prohl (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Institut für Mathematik [Berlin]
3 Mathematisches Institut [Tübingen]

We investigate existence and uniqueness for the 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 Gyöngy-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 × H 1 .

Mots clés: stochastic partial differential equations; liquid crystals; non-linear parabolic equations; harmonic maps Mathematics Subject Classification -60H15; 76A15; 35K55; 58E20

Domaines: Mathématiques [math]

Anne de Bouard, Antoine Hocquet, Andreas Prohl. EXISTENCE, UNIQUENESS AND REGULARITY FOR THE STOCHASTIC ERICKSEN-LESLIE EQUATION. Nonlinearity, inPress, ⟨10.1088/1361-6544/ac022e⟩. ⟨hal-03019167⟩