Controllability of systems of Stokes equations with one control force : existence of insensitizing controls
Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation
We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [Calderer et al., SIAM J. Math. Anal.33 (2002) 1033–1047], which is a special case of Ericksen's general continuum model in [Ericksen, Arch. Ration. Mech. Anal.113 (1991) 97–120]. We prove the global existence of weak solutions by passing to the limit in a regularized system. Moreover, we propose a practical...
Convergence of the rotating fluids system in a domain with rough boundaries
We consider a rotating fluid in a domain with rough horizontal boundaries. The Rossby number, kinematic viscosity and roughness are supposed of characteristic size . We prove a convergence theorem on solutions of Navier-Stokes Coriolis equations, as goes to zero, in the well prepared case. We show in particular that the limit system is a two-dimensional Euler equation with a nonlinear damping term due to boundary layers. We thus generalize the results obtained on flat boundaries with the classical...
Convergence results for MHD system.
Convergence to stationary solutions in a model of self-gravitating systems
We study convergence of solutions to stationary states in an astrophysical model of evolution of clouds of self-gravitating particles.
Convergence towards self-similar asymptotic behavior for the dissipative quasi-geostrophic equations
This work proves the convergence in L¹(ℝ²) towards an Oseen vortex-like solution to the dissipative quasi-geostrophic equations for several sets of initial data with suitable decay at infinity. The relative entropy method applies in a direct way for solving this question in the case of signed initial data and the difficulty lies in showing the existence of unique global solutions for the class of initial data for which all properties needed in the entropy approach are met. However, the estimates...
Corrections to the article “The multivelocity Peierls potential in the problem of refining the classical fundamental acoustic potential near the source of sound in a homogeneous Maxwellian gas”.
Couches d’Ekman pour les fluides tournants et la limite du système de Navier-Stokes vers celui d’Euler.
Coupling the equation for filtration flow to a first-order conservation law on the boundary
Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations
This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity and nonlinear source terms of the form and lying in L1. Some existence results are shown in this paper, including -estimates and positivity for both θ and φ.