The Gaussian Structure of the Stochastically Forced Burgers Equation and related problems

Abstract: I will explain some recent results which show that the law of the stochastic burgers equation at a fixed time t is absolutely continuous with respect to the natural Gaussian measure on the spatial domain. The results will apply to forcing just up to the point where the roughness of the forcing corresponds to the classical KPZ equation in the Burgers setting. As one approaches this level of roughness, the equations must be understood in as a Singular SPDEs (in the sense of Hairer ). As such the construction helps illuminate the structure of the equation and makes clear in what sense we might call these equations “truly” elliptic in this infinite dimensional setting. I will also make comments connecting back to previous results on the 2D Naiver Stokes equation. This work is joint with Marco Romito and Langxuan Su and builds on work with Andrea Watkins Hairston.

analysis of PDEsprobability

Audience: researchers in the discipline

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Stochastic PDEs and their friends

Series comments: We are organizing a three day online workshop devoted to recent developments in SPDEs and related topics. Please complete the registration form at forms.gle/G9Xw942iVNNgB4SLA if you would like to take part in the conference.

Confirmed speakers:

Yuri BAKHTIN (NYU)

Ajay CHANDRA (Imperial)

Dan CRISAN (Imperial)

Nina HOLDEN (ETH Zurich)

Kostantin KHANIN (U Toronto)

Davar KHOSHNEVISAN (University of Utah)

Nicolai KRYLOV (University of Minnesota)

Jonathan MATTINGLY (Duke)

Leonid MYTNIK (Technion)

Nicolas PERKOWSKI (Free U Berlin)

Ellen POWELL (Durham University)

Jeremy QUASTEL (U Toronto)

Daniel REMENIK (Universidad de Chile)

Armen SHIRIKYAN (University of Cergy-Pontoise)

Gigliola STAFFILANI (MIT)

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