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On weak solutions of steady Navier-Stokes equations for monatomic gas

Jan Březina, Antonín Novotný (2008)

Commentationes Mathematicae Universitatis Carolinae

We use L ∞ estimates for the inverse Laplacian of the pressure introduced by Plotnikov, Sokolowski and Frehse, Goj, Steinhauer together with the nonlinear potential theory due to Adams, Hedberg, to get a priori estimates and to prove existence of weak solutions to steady isentropic Navier-Stokes equations with the adiabatic constant γ > 1 3 ( 1 + 13 ) ≈ 1 . 53 for the flows powered by volume non-potential forces and with γ > 1 8 ( 3 + 41 ) ≈ 1 . 175 for the flows powered by potential forces and arbitrary non-volume forces. According to our knowledge,...

On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality

Joachim Naumann (2008)

Banach Center Publications

We consider the non-stationary Navier-Stokes equations completed by the equation of conservation of internal energy. The viscosity of the fluid is assumed to depend on the temperature, and the dissipation term is the only heat source in the conservation of internal energy. For the system of PDE's under consideration, we prove the existence of a weak solution such that: 1) the weak form of the conservation of internal energy involves a defect measure, and 2) the equality for the total energy is satisfied....

Ondes de surface faiblement non-linéaires

Sylvie Benzoni-Gavage, Jean-François Coulombel, Nikolay Tzvetkov (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

Cet exposé concerne l’approximation faiblement non-linéaire de problèmes aux limites invariants par changement d’échelles.

Ondes progressives pour l’équation de Gross-Pitaevskii

Fabrice Béthuel, Philippe Gravejat, Jean-Claude Saut (2007/2008)

Séminaire Équations aux dérivées partielles

Cet exposé présente les résultats de l’article [3] au sujet des ondes progressives pour l’équation de Gross-Pitaevskii : la construction d’une branche d’ondes progressives non constantes d’énergie finie en dimensions deux et trois par un argument variationnel de minimisation sous contraintes, ainsi que la non-existence d’ondes progressives non constantes d’énergie petite en dimension trois.

Operator-splitting and Lagrange multiplier domain decomposition methods for numerical simulation of two coupled Navier-Stokes fluids

Didier Bresch, Jonas Koko (2006)

International Journal of Applied Mathematics and Computer Science

We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid...

Optical leptons.

Kovachev, Lubomir M. (2004)

International Journal of Mathematics and Mathematical Sciences

Optimal boundary control for hyperdiffusion equation

Hanif Heidari, Alaeddin Malek (2010)

Kybernetika

In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain...

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