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math.AP2026
Local-in-Time Existence of solutions to the Gravity Water Wave Kinetic Equation
Yulin Pan, Xiaoxu Wu
In this paper, we study the Cauchy problem for the four-wave kinetic equation describing the weak turbulence of gravity water waves. The mathematical challenges of this analysis st…
math.AP2021★ 3 cited
Energy transfer for solutions to the nonlinear Schrödinger equation on irrational tori
Alexander Hrabski, Yulin Pan, Gigliola Staffilani +1
We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schrödinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the analytic st…