Randomization in nonlinear PDE and the supercritical periodic quintic NLS in 3D.
speaker: Gigliola Staffilani (MIT)abstract: In the last two decades significant progress has been made in the study of nonlinear dispersive and wave equations, settling questions about existence of solutions, their long time behavior, and singularity formation. The thrust of this body of work has focused primarily on deterministic aspects of wave phenomena, where sophisticated tools from nonlinear Fourier analysis, geometry, and also analytic number theory have played a crucial role in the underlying methods. Yet &nb sp;some important obstacles and open questions remain. A natural approach to overcome these, and one which has recently seen a growing interest, is to consider certain evolution equations from a non-deterministic point of view (e.g. the random data Cauchy problem ) and incorporate powerful tools from probability as well. In this talk we will explain some of these ideas and describe recent works on the almost sure well-posedness for the 3D periodic quintic nonlinear Schrodinger equation below the critical energy space (joint with A. Nahmod) and f or the almost sure existence of weak solutions for the 3D periodic Navier-Stokes equation below the L2 norm (joint with N. Pavlovic and A. Nahmod).
timetable:
Thu 23 May, 10:00 - 10:50, Aula Dini
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