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8 papers · 1 filter
Nonlinear Forward-Backward Problems
Anne-Laure Dalibard, Frédéric Marbach, Jean Rax
We prove the existence and uniqueness of strong solutions to the equation in the vicinity of the linear shear flow, subject to perturbations of the source term…
Profile decomposition and scattering for general nonlinear Schr{ö}dinger equations
Thomas Duyckaerts, Phan van Tin
We consider a Schr{ö}dinger equation with a nonlinearity which is a general perturbation of a power'' nonlinearity. We construct a profile decomposition adapted to this nonlinearit…
Improved Fractal Weyl upper bound in obstacle scattering
Lucas Vacossin
In this paper, we are interested in the problem of scattering by strictly convex obstacles in the plane. We provide an upper bound for the number of resonances in the box…
Spectral summability for the quartic oscillator with applications to the Engel group
Hajer Bahouri, Davide Barilari, Isabelle Gallagher +1
In this article, we investigate spectral properties of the sublaplacian on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approac…
Stability of a cross-diffusion system and approximation by repulsive random walks: a duality approach
Vincent Bansaye, Ayman Moussa, Felipe Muñoz-Hernández
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimat…
Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian
Louise Gassot, Mickaël Latocca
We study the local well-posedness of the nonlinear Schrödinger equation associated to the Grushin operator with random initial data. To the best of our knowledge, no well-posedness…