Search results
On the implosion of a three dimensional compressible fluid. 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 infinite density) at a later time at ...
Dec 7, 2022 · A team of four mathematicians, including Frank Merle, holder of the CY Cergy Paris Université-IHES Chair in Analysis, Pierre Raphaël, holder of the Schlumberger Chair for mathematical sciences at IHES and Professor at the University of Cambridge, Igor Rodnianski, Professor at Princeton University, and Jérémie Szeftel, CNRS Research Director at Sorbonne Université and a regular visitor of ...
We would like to show you a description here but the site won’t allow us.
Oct 8, 2006 · Authors: Carlos E.Kenig, Frank Merle View a PDF of the paper titled Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case, by Carlos E.Kenig and Frank Merle
Feb 17, 2004 · We consider finite time blow-up solutions to the critical nonlinear Schrödinger equation iu t =-Δu-|u|4/N u with initial condition u 0∈H 1. Existence of such solutions is known, but the complete blow-up dynamic is not understood so far. For a specific set of initial data, finite time blow-up with a universal sharp upper bound on the blow-up rate has been proved in [22], [23].We establish ...
CHARLES COLLOT, FRANK MERLE, AND PIERRE RAPHAËL Abstract. We consider the energy critical semilinear heat equation ∂tu= ∆u+ |u| 4 d−2u, x∈ Rd and give a complete classification of the flow near the ground state solitary wave Q(x) = 1 1 + |x|2 d(d−2) d−2 2 in dimension d≥ 7, in the energy critical topology and without radial ...
Frank Merle, Pierre Raphaël, Igor Rodnianski, Jeremie Szeftel To cite this version: Frank Merle, Pierre Raphaël, Igor Rodnianski, Jeremie Szeftel. On the implosion of a compress-ible fluid I: Smooth self-similar inviscid profiles. Annals of Mathematics, 2022, 196 (2), pp.567-778. 10.4007/annals.2022.196.2.3. hal-03796687
