arXiv subjects

Louis Tebou

Publications and source records attributed to Louis Tebou.

3 recordsLinked to original sources

arXiv2022

Energy decay estimates for the wave equation with supercritical nonlinear damping

We consider a damped wave equation in a bounded domain. The damping is nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that the energy of the strong solution in the supercritical case decays as a negative power of t; the rate of decay is the same as in the subcritical or critical cases, provided that the space dimension does not exceed ten. Next, relying on a new differential inequality, we show that if the initial displacement is further required to lie in L p , then the energy of the corresponding weak solution decays logarithmically in the supercritical case. Those new results complement those in the literature and open an important breach in the unknown land of super-critical damping mechanisms.

math.AP↗

arXiv2021

Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case

In this paper, we examine regularity issues for two damped abstract elastic systems; the damping and coupling involve fractional powers $\mu, \theta$, with $0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix defining the coupling and damping is nondegenerate. This new work is a sequel to the degenerate case that we discussed recently in \cite{kfl}. First, we prove that for $1/2 \leq \mu , \theta \leq 1$, the underlying semigroup is analytic. Next, we show that for $\min(\mu,\theta) \in (0,1/2)$, the semigroup is of certain Gevrey classes. Finally, some examples of application are provided.

math.AP↗

arXiv2015

On a regularized family of models for the full Ericksen-Leslie system

We consider a general family of regularized systems for the full Ericksen-Leslie model for the hydrodynamics of liquid crystals in $n$-dimensional compact Riemannian manifolds, $n$=2,3. The system we consider consists of a regularized family of Navier-Stokes equations (including the Navier Stokes-$α$-like equation, the Leray-$α$ equation, the Modified Leray-$α$ equation, the Simplified Bardina model, the Navier Stokes-Voigt model and the Navier-Stokes equation) for the fluid velocity $u$ suitably coupled with a parabolic equation for the director field $d$. We establish existence, stability and regularity results for this family. We also show the existence of a finite dimensional global attractor for our general model, and then establish sufficiently general conditions under which each trajectory converges to a single equilibrium by means of a Lojasiewicz-Simon inequality.

math.AP↗