Well-posedness of stochastic second grade fluids

Well-Posedness for the Dumbbell Model of Polymeric Fluids

The dumbbell model is a coupled hydrodynamic-kinetic model for polymeric fluids in which the configurations of the dumbbells are described by stochastic differential equations. We prove well-posedness of this model by deriving directly a priori estimates on the stochastic model. Our results can be used to analyze stochastic simulation methods such as the ones that are based on Brownian configur...

Well-posedness in critical spaces for barotropic viscous fluids

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improve the analysis of R. Danchin in [13], by the fact that we choose initial density more general in B N p p,1 with 1 ≤ p < +∞. Our result relies on a new a priori estimate for the velocity, whe...

Local well-posedness results for density-dependent incompressible fluids

This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in R with N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity and we aim at stating well-posedness in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon...

Weak Solutions of a Stochastic Model for Two-Dimensional Second Grade Fluids

Well-posedness of Second Order Evolution Equation on Discrete Time

We characterize the well-posedness for second order discrete evolution equations in UMD spaces by means of Fourier multipliers and R-boundedness properties of the resolvent operator which defines the equation. Applications to semilinear problems are given.