On the Splash Singularity for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic equations in 3D
Guangyi HongTao LuoZhonghao Zhao
Guangyi HongTao LuoZhonghao Zhao
Sep 2023
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摘要原文
In this paper, the existence of finite-time splash singularity is proved for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic (MHD) equations in $ \mathbb{R}^{3}$, based on a construction of a sequence of initial data alongside delicate estimates of the solutions. The result and analysis in this paper generalize those by Coutand and Shkoller in [14, Ann. Inst. H. Poincar\'{e} C Anal. Non Lin\'{e}aire, 2019] from the viscous surface waves to the viscous conducting fluids with magnetic effects for which non-trivial magnetic fields may present on the free boundary. The arguments in this paper also hold for any space dimension $d\ge 2$.
