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On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Piotr Mucha, Wojciech Zajączkowski (2000)

Applicationes Mathematicae

The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that u W r 2 , 1 ( Ω ˜ T ) with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the L p -approach the Lagrangian coordinates must be used. We are looking...

On some parabolic-elliptic system with self-similar pressure term

Robert Stańczy (2006)

Banach Center Publications

A priori estimates for solutions of a system describing the interaction of gravitationally attracting particles with a self-similar pressure term are proved. The presented theory covers the case of the model with diffusions that obey either Fermi-Dirac statistics or a polytropic one.

On the linear force-free fields in bounded and unbounded three-dimensional domains

Tahar-Zamène Boulmezaoud, Yvon Maday, Tahar Amari (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.

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