On the instability of solitary-wave solutions for fifth-order water wave models.
On the instantaneous spreading for the Navier–Stokes system in the whole space
We consider the spatial behavior of the velocity field of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of . We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the Instantaneous Spreading for the Navier–Stokes System in the Whole Space
We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space () for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.
On the limit amplitude principle for a layer.
On the long time behavior of KdV type equations
In a series of recent papers, Martel and Merle solved the long-standing open problem on the existence of blow up solutions in the energy space for the critical generalized Korteweg- de Vries equation. Martel and Merle introduced new tools to study the nonlinear dynamics close to a solitary wave solution. The aim of the talk is to discuss the main ideas developed by Martel-Merle, together with a presentation of previously known closely related results.
On the long time behaviour of solutions of a class of autonomous reaction-diffusion systems.
On the long-time behaviour of solutions of the p-Laplacian parabolic system
Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be , and in the variable exponent case, L² and -weak.
On the low frequency asymptotics in electromagnetic theory.
On the Neumann problem of one-dimensional nonlinear thermoelasticity with time-independent external forces
On the NLS dynamics for infinite energy vortex configurations on the plane.
On the nonlinear stabilization of the wave equation
We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.
On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
On the PC-ansatz.
On the quasi-classical asymptotics of the forward scattering amplitude and of the total scattering cross-section
On the quenching of solutions of the wave equation with a nonlinear boundary condition.
On the regular solutions for some classes of Navier-Stokes equations
On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations
On the Schrödinger heat kernel in horn-shaped domains
We prove pointwise lower bounds for the heat kernel of Schrödinger semigroups on Euclidean domains under Dirichlet boundary conditions. The bounds take into account non-Gaussian corrections for the kernel due to the geometry of the domain. The results are applied to prove a general lower bound for the Schrödinger heat kernel in horn-shaped domains without assuming intrinsic ultracontractivity for the free heat semigroup.
On the singular behavior of solutions of a transmission problem in a dihedral.