2019/06/13 by Daniel Han-Kwan, Han-Kwan, Daniel, Toan T. Nguyen +3 · 4 citations
Engineering · Mathematics · #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions #math.AP
paper · pdf · doi:10.48550/arxiv.1906.05723
25 pages, minor typos fixed
arxiv created 2019/07/10 · arxiv updated 2019/07/11
We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov-Poisson systems with screened interactions in the whole space ℝd (for d≥3) that was first established by Bedrossian, Masmoudi and Mouhot. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in Bedrossian at al. (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.