147 citations · 252 across the 17 of their papers we have counts for
24 papers
A quantitative averaging lemma for spatially dependent vector fields
Paul Alphonse, Billel Guelmame, Julien Vovelle
We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations ab…
A Smoluchowski-Kramers approximation for the stochastic variational wave equation
Billel Guelmame, Julien Vovelle
We investigate the Smoluchowski-Kramers approximation for the one-dimensional periodic variational wave equation with state-dependent damping and additive noise. We show that weak…
Global solutions to quadratic systems of stochastic reaction-diffusion equations in space-dimension two
Marta Leocata, Julien Vovelle
We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a -estim…
Global dissipative martingale solutions to the variational wave equation with stochastic forcing
Billel Guelmame, Julien Vovelle
We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existe…
Diffusion-approximation for a kinetic spray-like system with random forcing
Arnaud Debussche, Angelo Rosello, Julien Vovelle
We study a kinetic toy model for a spray of particles immersed in an ambient fluid, subject to some additional random forcing given by a mixing, space-dependent Markov process. Usi…
The Boltzmann equation with an external force on the torus: Incompressible Navier-Stokes-Fourier hydrodynamical limit
Marc Briant, Arnaud Debussche, Julien Vovelle
We study the Boltzmann equation with external forces, not necessarily deriving from a potential, in the incompressible Navier-Stokes perturbative regime. On the torus, we establish…