Convergence of solutions of generalized Korteweg-de Vries-Burgers equations to those of first order equations
Convergence of the 'relativistic' heat equation to the heat equation as c → ∞.
We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light c tends to ∞ for any initial condition u0 ≥ 0 in L1(RN) ∩ L∞(RN).
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 of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.
Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
In this paper, we prove the convergence of the current defined from the Schrödinger-Poisson system with the presence of a strong magnetic field toward a dissipative solution of the Euler equations.
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...
Convolution of radius functions on ℝ³
We reduce the convolution of radius functions to that of 1-variable functions. Then we present formulas for computing convolutions of an abstract radius function on ℝ³ with various integral kernels - given by elementary or discontinuous functions. We also prove a theorem on the asymptotic behaviour of a convolution at infinity. Lastly, we deduce some estimates which enable us to find the asymptotics of the velocity and pressure of a fluid (described by the Navier-Stokes equations) in the boundary...
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.
Counterexample to Regularity for the Complex Monge-Ampère Equation.
Couplage des équations de Navier-Stokes et de la chaleur : le modèle et son approximation par éléments finis
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
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.
Covariant functional quantizations of superstrings
Covolume techniques for anisotropic media.
C?-Regularity for the Porous Medium Equation.
Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin's condition
Let u be a weak solution of the Navier-Stokes equations in a smooth bounded domain Ω ⊆ ℝ³ and a time interval [0,T), 0 < T ≤ ∞, with initial value u₀, external force f = div F, and viscosity ν > 0. As is well known, global regularity of u for general u₀ and f is an unsolved problem unless we pose additional assumptions on u₀ or on the solution u itself such as Serrin’s condition where 2/s + 3/q = 1. In the present paper we prove several local and global regularity properties by using assumptions...