Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the motion of free interface in ideal incompressible MHD   For the free boundary problem of the plasma-vacuum interface to
three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori
estimates of smooth solutions are proved in Sobolev norms by adopting a
geometrical point of view and some quantities such as the second fundamental
form and the velocity of the free interface are estimated. In the vacuum
region, the magnetic fields are described by the div-curl system of pre-Maxwell
dynamics, while at the interface the total pressure is continuous and the
magnetic fields are tangent to the interface, but we do not need any
restrictions on the size of the magnetic fields on the free interface. We
introduce the "virtual particle" endowed with a virtual velocity field in
vacuum to reformulate the problem to a fixed boundary problem under the
Lagrangian coordinates. The $L^2$-norms of any order covariant derivatives of
the magnetic fields both in vacuum and on the boundaries are bounded in terms
of initial data and the second fundamental forms of the free interface and the
rigid wall. The estimates of the curl of the electric fields in vacuum are also
obtained, which are also indispensable in elliptic estimates.

21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn