Hörmander's theorem for semilinear SPDEs

DOI10.1214/19-EJP387zbMath1462.60084arXiv1811.06339MaRDI QIDQ2279327

Andris Gerasimovičs, Martin Hairer

Publication date: 12 December 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.06339

zbMATH Keywords

rough pathsrough PDEsHörmander's conditionrough Fubini theorem

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Navier-Stokes equations (35Q30) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (22)

Non-autonomous rough semilinear PDEs and the multiplicative sewing lemma ⋮ Unstable manifolds for rough evolution equations ⋮ Unstable manifolds for rough evolution equations ⋮ Higher moments for the stochastic Cahn–Hilliard equation with multiplicative Fourier noise ⋮ Local zero-stability of rough evolution equations ⋮ A priori bounds for rough differential equations with a non-linear damping term ⋮ The Gaussian structure of the singular stochastic Burgers equation ⋮ Stochastic evolution equations with rough boundary noise ⋮ A Fubini type theorem for rough integration ⋮ Malliavin calculus and densities for singular stochastic partial differential equations ⋮ Center manifolds for rough partial differential equations ⋮ Random attractors for rough stochastic partial differential equations ⋮ Existence of smooth stable manifolds for a class of parabolic SPDEs with fractional noise ⋮ Nonuniqueness in law of stochastic 3D Navier-Stokes equations ⋮ An Itô formula for rough partial differential equations and some applications ⋮ New directions in rough path theory. Abstracts from the workshop held December 6--12, 2020 (online meeting) ⋮ Smoothness of densities for path-dependent SDEs under Hörmander's condition ⋮ Generalized Burgers equation with rough transport noise ⋮ Existence of densities for stochastic evolution equations driven by fractional Brownian motion ⋮ Besov rough path analysis (with an appendix by Pavel Zorin-Kranich) ⋮ Global solutions for semilinear rough partial differential equations ⋮ Mild stochastic sewing lemma, SPDE in random environment, and fractional averaging

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