Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Patricio Cumsille; Takéo Takahashi

Displaying similar documents to “Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid”

On the motion of rigid bodies in a viscous fluid

Eduard Feireisl (2002)

Applications of Mathematics

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We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying $ℝ^{2}$ . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Steady compressible Navier-Stokes-Fourier system in two space dimensions

Petra Pecharová, Milan Pokorný (2010)

Commentationes Mathematicae Universitatis Carolinae

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We study steady flow of a compressible heat conducting viscous fluid in a bounded two-dimensional domain, described by the Navier-Stokes-Fourier system. We assume that the pressure is given by the constitutive equation $p (ρ, θ) \sim ρ^{γ} + ρ θ$ , where $ρ$ is the density and $θ$ is the temperature. For $γ > 2$ , we prove existence of a weak solution to these equations without any assumption on the smallness of the data. The proof uses special approximation of the original problem, which guarantees the pointwise boundedness...

A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum

Jens Frehse, Sonja Goj, Josef Málek (2005)

Applications of Mathematics

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We consider a continuum model describing steady flows of a miscible mixture of two fluids. The densities $ρ_{i}$ of the fluids and their velocity fields $u^{(i)}$ are prescribed at infinity: $ρ_{i} |_{\infty} = ρ_{i \infty} > 0$ , $u^{(i)} |_{\infty} = 0$ . Neglecting the convective terms, we have proved earlier that weak solutions to such a reduced system exist. Here we establish a uniqueness type result: in the absence of the external forces and interaction terms, there is only one such solution, namely $ρ_{i} \equiv ρ_{i \infty}$ , $u^{(i)} \equiv 0$ , $i = 1, 2$ .