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Mathematical Physics Seminar

Geometric Wave Equations and Random data

Sagun Chanillo - Rutgers University

Location:  Hill Center Room 705
Date & time: Thursday, 24 February 2022 at 12:00PM - 1:00PM

Abstract: We will introduce two types of wave equations whose elliptic parts arise from Geometric problems, the problem of uniformization or prescribing Gauss Curvature on the 2-sphere, and the problem of prescribing Mean curvature for a surface. The corresponding elliptic equations have been studied by Moser, A. Chang and Paul Yang, H. Brezis and Coron. Next we study the initial value problem associated to the wave equation which has quadratic growth in the gradient. By randomizing the initial data in the spirit of J. Lebowitz, H. Rose and E. Speer, we manage to show all the iterates of the solutions exist. Previously it was known that even the first iterate blows up by an example of Zhou. This is joint work with M. Czubak, D. Mendelson, A. Nahmod and G. Staffiliani.

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