Displaying similar documents to “Local existence of solutions of a free boundary problem for equations of compressible viscous heat-conducting fluids”

Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids

G. Ströhmer, W. Zajączkowski (1999)

Applicationes Mathematicae

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Local existence of solutions is proved for equations describing the motion of a viscous compressible barotropic and self-gravitating fluid in a domain bounded by a free surface. First by the Galerkin method and regularization techniques the existence of solutions of the linearized momentum equations is proved, next by the method of successive approximations local existence to the nonlinear problem is shown.

On local motion of a compressible barotropic viscous fluid bounded by a free surface

W. Zajączkowski (1992)

Banach Center Publications

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We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the...

On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

Wojciech M. Zajączkowski

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We consider the motion of a viscous compressible barotropic fluid in ℝ 3 bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes...

Global and exponential attractors for a Caginalp type phase-field problem

Brice Bangola (2013)

Open Mathematics

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We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.