6 papers
Asymptotic Growth and Decay of Two-Dimensional Symmetric Plasmas
Jonathan Ben-Artzi, Baptiste Morisse, Stephen Pankavich
We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric init…
Uniform convergence in von Neumann's ergodic theorem in the absence of a spectral gap
Jonathan Ben-Artzi, Baptiste Morisse
Von Neumann's original proof of the ergodic theorem is revisited. A uniform convergence rate is established under the assumption that one can control the density of the spectrum of…
On hyperbolicity and Gevrey well-posedness. Part three: a class of weakly hyperbolic systems
Baptiste Morisse
We consider a class of weakly hyperbolic systems of first-order, nonlinear PDEs. Weak hyperbolicity means here that the principal symbol of the system has a crossing of eigenvalues…
On the action of pseudo-differential operators on Gevrey spaces
Baptiste Morisse
In this paper we study the action of pseudo-differential operators acting on Gevrey spaces. We introduce classes of classical symbols with spatial Gevrey regularity. As the spatial…
On hyperbolicity and Gevrey well-posedness. Part two: Scalar or degenerate transitions
Baptiste Morisse
For first-order quasi-linear systems of partial differential equations, we formulate an assumption of a transition from initial hyperbolicity to ellipticity. This assumption bears…
On hyperbolicity and Gevrey well-posedness. Part one: the elliptic case
Baptiste Morisse
In this paper we prove that the Cauchy problem for first-order quasi-linear systems of partial differential equations is ill-posed in Gevrey spaces, under the assumption of an init…