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Displaying similar documents to “Identifiability and stability of boundaries in a supercritical free surface flow.”

Some recent results on the Muskat problem

Angel Castro, Diego Córdoba, Francisco Gancedo (2010)

Journées Équations aux dérivées partielles

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We consider the dynamics of an interface given by two incompressible fluids with different characteristics evolving by Darcy’s law. This scenario is known as the Muskat problem, being in 2D mathematically analogous to the two-phase Hele-Shaw cell. The purpose of this paper is to outline recent results on local existence, weak solutions, maximum principles and global existence.

On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid

Ewa Zadrzyńska, Wojciech M. Zajączkowski (1996)

Annales Polonici Mathematici

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We consider the motion of a viscous compressible heat conducting fluid in ℝ³ bounded by a free surface which is under constant exterior pressure. Assuming that the initial velocity is sufficiently small, the initial density and the initial temperature are close to constants, the external force, the heat sources and the heat flow vanish, we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.

Non-parallel plane Rayleigh Benard convection in cylindrical geometry

A. Golbabai (1995)

Applicationes Mathematicae

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This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form z = ε 2 g ( s ) , s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near...

Almost free splitters

Rüdiger Göbel, Saharon Shelah (1999)

Colloquium Mathematicae

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Let R be a subring of the rationals. We want to investigate self splitting R-modules G, that is, such that E x t R ( G , G ) = 0 . For simplicity we will call such modules splitters (see [10]). Also other names like stones are used (see a dictionary in Ringel’s paper [8]). Our investigation continues [5]. In [5] we answered an open problem by constructing a large class of splitters. Classical splitters are free modules and torsion-free, algebraically compact ones. In [5] we concentrated on splitters which...

Low regularity Cauchy theory for the water-waves problem: canals and swimming pools

T. Alazard, N. Burq, C. Zuily (2011)

Journées Équations aux dérivées partielles

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The purpose of this talk is to present some recent results about the Cauchy theory of the gravity water waves equations (without surface tension). In particular, we clarify the theory as well in terms of regularity indexes for the initial conditions as fin terms of smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developed in [, ], after suitable para-linearizations, the system can be arranged...