Random Versus Deterministic Approach in the Study of Wave and Dispersive Equations
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
PDE
dispersive
wave equation
NLS equation
p-NLS equation
well-posedness
mass critical - energy critical scales
almost sure well-posedness
invariant Gibbs measure
supercritical exponent
35B30 - Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]
35Q55 - NLS-like equations (nonlinear Schrödinger) [See also 37K10]
60A10 - Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
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The point of this talk is to show how certain well-posedness results that are not available using deterministic techniques involving Fourier and harmonic analysis
can be obtained when introducing randomization in the set of initial data. Along the way I will also prove a certain “probabilistic propagation of regularity” for certain almost sure globally well-posed dispersive equations. This talk is based on joint work with A. Nahmod
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14383
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