Splash singularity for the free boundary incompressible viscous MHD
arXiv:2304.06893 · doi:10.1016/j.jde.2023.10.001
Abstract
In this paper, we prove the existence of smooth initial data for the two-dimensional free boundary incompressible viscous magnetohydrodynamics (MHD) equations, for which the interface remains regular but collapses into a splash singularity (self-intersects in at least one point) in finite time. The existence of the splash singularities is guaranteed by a local existence theorem, in which we need suitable spaces for the modified magnetic field and modification of the velocity and the pressure such that the modified initial velocity is zero, and a stability result which allows us to construct a class of initial velocities and domains for an arbitrary initial magnetic field. It turns out that the presence of the magnetic field does not prevent the viscous fluid to form splash singularities for certain smooth initial data.
arXiv comment60 pages,9 figures. arXiv admin note: text overlap with arXiv:1806.11089 by other authors
References in corpus (6)
- On the finite-time splash and splat singularities for the 3-D free-surface Euler equations
- A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows
- Splash singularity for water waves
- Ill-posedness of free boundary problem of the incompressible ideal MHD
- A Regularity Result for the Incompressible Magnetohydrodynamics Equations with Free Surface Boundary
- Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics