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The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.
We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.
We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not...
We study in an abstract setting the indirect stabilization of systems of two wave-like
equations coupled by a localized zero order term. Only one of the two equations is
directly damped. The main novelty in this paper is that the coupling operator is not
assumed to be coercive in the underlying space. We show that the energy of smooth
solutions of these systems decays polynomially at infinity, whereas it is known that
exponential stability does not...
Dans ce travail, nous donnons une estimation logarithmique des
données de la solution u, d'un problème hyperbolique
avec condition aux limites de type Neumann, par la trace de u
restreinte à un ouvert du bord, pendant un temps suffisamment
grand qui nous permet d'estimer la fonction de coût de ce
problème.
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