18,715 research outputs found
A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows
In the present paper, we prove the a priori estimates of Sobolev norms for a
free boundary problem of the incompressible inviscid MHD equations in all
physical spatial dimensions and 3 by adopting a geometrical point of view
used in Christodoulou-Lindblad CPAM 2000, and estimating quantities such as the
second fundamental form and the velocity of the free surface. We identify the
well-posedness condition that the outer normal derivative of the total pressure
including the fluid and magnetic pressures is negative on the free boundary,
which is similar to the physical condition (Taylor sign condition) for the
incompressible Euler equations of fluids.Comment: 34 page
Rotating Fluids with Self-Gravitation in Bounded Domains
In this paper, we study the steady solutions of Euler-Poisson equations in
bounded domains with prescribed angular velocity. This models a rotating
Newtonian star consisting of a compressible perfect fluid with given equation
of state . When the domain is a ball and the angular
velocity is constant, we obtain both existence and non-existence theorems,
depending on the adiabatic gas constant . In addition we obtain some
interesting properties of the solutions; e.g., monotonicity of the radius of
the star with both angular velocity and central density. We also prove that the
radius of a rotating spherically symmetric star, with given constant angular
velocity and constant entropy, is uniformly bounded independent of the central
density . This is physically striking and in sharp contrast to the case of the
nonrotating star. For general domains and variable angular velocities, both an
existence result for the isentropic equations of state and non-existence result
for the non-isentropic equation of state are also obtained.Comment: 37page
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