Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Raphael, Pierre"'
Based on recent ideas, stemming from the use of bubbles, we discuss an algorithm for the numerical simulation of the cubic nonlinear Schr{\"o}dinger equation with harmonic potential in any dimension, which could be easily extended to other polynomial
Externí odkaz:
http://arxiv.org/abs/2303.13969
Autor:
Faou, Erwan, Raphael, Pierre
We introduce specific solutions to the linear harmonic oscillator, named bubbles. They form resonant families of invariant tori of the linear dynamics, with arbitrarily large Sobolev norms. We use these modulated bubbles of energy to construct a clas
Externí odkaz:
http://arxiv.org/abs/2006.08206
We consider the energy supercritical defocusing nonlinear Schr\"odinger equation $i\partial_tu+\Delta u-u|u|^{p-1}=0$ in dimension $d\ge 5$. In a suitable range of energy supercritical parameters $(d,p)$, we prove the existence of $\mathcal C^\infty$
Externí odkaz:
http://arxiv.org/abs/1912.11005
We consider the barotropic Euler equations in dimension d>1 with decaying density at spatial infinity. The phase portrait of the nonlinear ode governing the equation for spherically symmetric self-similar solutions has been introduced in the pioneeri
Externí odkaz:
http://arxiv.org/abs/1912.10998
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with i
Externí odkaz:
http://arxiv.org/abs/1912.11009
We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schr\"odinger equation $i\partial_t u + \Delta u + |u|^{p-1}u=0$ on $\mathbf{R}^d$, close to the mass critical case and for any space dimension $d\ge 1
Externí odkaz:
http://arxiv.org/abs/1911.11457
Autor:
Abel Gomez-Caceres, Iskandar Tamimi-Mariño, Francisco Javier Martinez-Malo, Raphael Pierre Idiart-Charrier, Ignacio Vieitez-Riestra, Ivan Medina-Porqueres
Publikováno v:
Journal of Clinical Medicine, Vol 13, Iss 5, p 1501 (2024)
(1) Purpose: The incidence of anterior cruciate ligament (ACL) ruptures in children and adolescents has considerably increased during the last decades due to higher levels of competitive athletic activity, and early sport specialization and professio
Externí odkaz:
https://doaj.org/article/026b62cf68a9408cabcbd42184216df3
Autor:
Naumkin, Ivan, Raphaël, Pierre
We consider the mass critical fractional (NLS). We show the existence of travelling waves for all mass below the ground state mass, and give a complete description of the associated profiles in the small mass limit. We therefore recover a situation s
Externí odkaz:
http://arxiv.org/abs/1712.04484
We consider the energy super critical $d+1$ dimensional semilinear heat equation $$\partial_tu=\Delta u+u^{p}, \ \ x\in \Bbb R^{d+1}, \ \ p\geq 3, \ d\geq 14.$$ A fundamental open problem on this canonical nonlinear model is to understand the possibl
Externí odkaz:
http://arxiv.org/abs/1709.04941
We consider the energy super critical 4 dimensional semilinear heat equation $$\partial_tu=\Delta u+|u|^{p-1}u, \ \ x\in \Bbb R^4, \ \ p>5.$$ Let $\Phi(r)$ be a three dimensional radial self similar solution for the three supercritical probmem as exh
Externí odkaz:
http://arxiv.org/abs/1709.04939