DYNAMICS NEAR THE GROUND STATE FOR THE ENERGY CRITICAL NONLINEAR HEAT EQUATION IN LARGE DIMENSIONS

Recall the following parabolic regularizing effect due to Brezis-Cazenave that we will use to obtain a locally (in time) bounded solution to (4) with singular data...

If, in addition, we assume that the critical norm of the evolution localized to the light cone (the forward light cone in the case of global solutions and the backwards cone in the

- Higher order terms in the equation of state are derived and studied numerically for the Ising model, A brief comparison is made with corresponding results for exactly

This paper gives a simple proof of the Wirsching-Goodwin representation of integers connected to 1 in the 3x+1 problem (see [5] and [2]).. The 3x + 1 problem asks whether, starting

In the case of the Schr¨odinger equation, one obtains Strichartz estimates on a semiclassical time scale (taking advantage of a finite speed of propagation principle at this scale),

We prove the uniqueness of weak solutions to the critical defocusing wave equation in 3D under a local energy inequality condition.. Uniqueness was proved only under an

If, in addition, we assume that the critical norm of the evolution localized to the light cone (the forward light cone in the case of global solutions and the backwards cone in the

Zhao, Global well-posedness and scattering for the defocusing energy critical nonlinear Schr¨ odinger equations of fourth-order in the radial case, J. Zhao, Global well-posedness