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On blow up for the energy super critical defocusing non linear Schrödinger equations
Frank Merle, Pierre Raphael, Igor Rodnianski +1
We consider the energy supercritical defocusing nonlinear Schrödinger equation in dimension . In a suitable range of energy supercritical par…
On smooth self similar solutions to the compressible Euler equations
Frank Merle, Pierre Raphael, Igor Rodnianski +1
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 sphericall…
Soliton resolution for the radial critical wave equation in all odd space dimensions
Thomas Duyckaerts, Carlos E. Kenig, Frank Merle
Consider the energy-critical focusing wave equation in odd space dimension . The equation has a nonzero radial stationary solution , which is unique up to scaling and s…
Decay estimates for nonradiative solutions of the energy-critical focusing wave equation
Thomas Duyckaerts, Carlos E. Kenig, Frank Merle
Consider the energy-critical focusing wave equation in space dimension . The equation has a nonzero radial stationary solution , which is unique up to scaling and sign…
On the implosion of a three dimensional compressible fluid
Frank Merle, Pierre Raphael, Igor Rodnianski +1
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 f…
Exterior energy bounds for the critical wave equation close to the ground state
Thomas Duyckaerts, Carlos E. Kenig, Frank Merle
By definition, the exterior asymptotic energy of a solution to a wave equation on is the sum of the limits as of the energy in the the exterior…