【online】On magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids......
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题目：On magnetic inhibition theory in 3D non-resistive magnetohydrodynamic fluids: Global existence of large solutions（I)、(II)
时间：2022年9月18日 上午10:30-12:30 下午 2:30-4:30
摘要: This talk is mainly concerned with the global existence and asymptotic behaviour of classical
solutions to the three-dimensional (3D) incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in a 3D periodic domain (in Lagrangian coordinates). Motivated by the approximate theory of the ideal MHD equations in , the Diophantine condition imposed in  and the magnetic inhibition mechanism in the version of Lagrangian coordinates analyzed in , we prove the global existence of a unique classical solution with some class of large initial perturbations, where the intensity of impressed magnetic fields depends increasingly on the H17 X H21-norm of the initial velocity and magnetic field perturbations. Our result not only mathematically verifies that a strong impressed magnetic field can prevent the singularity formation of classical solutions with large initial data in the viscous MHD case, but also provides a starting point for the existence theory of large perturbation solutions to the 3D non-resistive viscous MHD equations. In addition, we also show that for large time or sufficiently strong impressed magnetic fields, the MHD equations converge to the corresponding linearized pressureless equations in the algebraic convergence-rates with respect to both time and field intensity.
(This is a joint-wrok with Prof. Fei Jiang from Fuzhou University)
1 C. Bardos, C. Sulem, P. Sulem, Longtime dynamics of a conductive fluid in the presence of a strong magnetic field, Trans. Am. Math. Soc. 305 (1988) 175--191.
2 J.J. Chen, T.Y. Hou, Finite time blowup of 2D Boussinesq and 3D Euler equations with C1,α velocity and boundary, Commun. Math. Phys. 383 (2021) 1559--1667.
3 F. Jiang, S. Jiang, On magnetic inhibition theory in non-resistive magnetohydrodynamic fluids, Arch. Rational Mech. Anal. 233 (2019) 749--798.