4 papers · 1 filter
Construction of log-log blowup solutions for the mass critical nonlinear Schrödinger equation
Chenjie Fan, Dana Mendelson
In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schrödinger equation on under rough but structured random perturbations at $L…
The focusing energy-critical nonlinear wave equation with random initial data
Carlos Kenig, Dana Mendelson
We consider the focusing energy-critical quintic nonlinear wave equation in three dimensional Euclidean space. It is known that this equation admits a one-parameter family of radia…
Scattering for defocusing energy subcritical nonlinear wave equations
Benjamin Dodson, Andrew Lawrie, Dana Mendelson +1
We consider the Cauchy problem for the defocusing power type nonlinear wave equation in -dimensions for energy subcritical powers in the range . We prove that…
Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation
Benjamin Dodson, Jonas Luhrmann, Dana Mendelson
We consider the Cauchy problem for the defocusing cubic nonlinear Schrödinger equation in four space dimensions and establish almost sure local well-posedness and conditional almos…