Seminar
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| Location: | SLMath: Online/Virtual |
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
Large-Time Behavior of 2D Incompressible MHD System with Partial Dissipation
To participate in this seminar, please register here: https://www.msri.org/seminars/25657
Abstract: In this talk, we will discuss the decay results on a 2D magnetohydrodynamic (MHD) system with only vertical dissipation. Without the magnetic field, the fluid velocity obeys a 2D anisotropic Navier-Stokes equation and is not known to be stable in the Sobolev setting H 2 due to the potential double exponential growth of its H 2 -norm in time. However, when coupled with the magnetic field in the MHD system, we show that the H 2 -norm of any perturbation near a background magnetic field actually decays algebraically in time.
This result demonstrates that the magnetic field indeed stabilizes and damps the electrically conducting fluids. Mathematically this result along with its proof offers a new and effective approach to the large-time behavior on partially dissipated systems of partial differential equations (PDEs). Existing methods are mostly designed for systems with full dissipation and do not apply when the dissipation is anisotropic. This is the joint work with Farzana
Hafeez and Jiahong Wu.
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