Ioakeim Ampatzoglou – “Global well-posedness of the inhomogeneous kinetic wave equation near vacuum”

Courant PIs Workshop 2022

Abstract: We discuss the global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersion relation in dimension d=2,3. Moreover, for non-negative initial data, the solution remains non-negative. This is achieved by connecting the inhomogeneous kinetic wave equation, for such dimensions, to the cubic part of a quantum Boltzmann-type equation with moderately hard potential and no collisional averaging.

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