Kazuo Yamazaki
Published 2023-08-18Version 1
We study the two-dimensional magnetohydrodynamics system forced by space-time white noise. Due to a lack of an explicit invariant measure, the approach of Da Prato and Debussche (2002, J. Funct. Anal., \textbf{196}, pp. 180--210) on the Navier-Stokes equations does not seem to fit. We follow instead the approach of Hairer and Rosati (2023, arXiv:2301.11059 [math.PR]), take advantage of the structure of Maxwell's equation, such as anti-symmetry, to find an appropriate paracontrolled ansatz and many crucial cancellations, and prove the global-in-time existence and uniqueness of its solution.
Behavior of solutions to the 1D focusing stochastic $L^2$-critical and supercritical nonlinear Schrödinger equation with space-time white noise
Remarks on the global regularity of two-dimensional magnetohydrodynamics system with zero dissipation
Global-in-time existence of perturbations around travelling-waves
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