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math.AP2024
Global well-posedness of the energy-critical stochastic nonlinear Schrödinger equation on the three-dimensional torus
Guopeng Li, Mamoru Okamoto, Liying Tao
We study the Cauchy problem of the defocusing energy-critical stochastic nonlinear Schrödinger equation (SNLS) on the three dimensional torus, forced by an additive noise. We adapt…
math.AP2023
Global well-posedness of the energy-critical stochastic Hartree nonlinear wave equation
Guopeng Li, Liying Tao, Tengfei Zhao
We consider the Cauchy problem for the stochastic Hartree nonlinear wave equations (SHNLW) with a cubic convolution nonlinearity and an additive stochastic forcing on the Euclidean…
math.AP2023
Almost sure scattering for defocusing energy critical Hartree equation on
Liying Tao, Tengfei Zhao
We consider the defocusing energy-critical Hartree equation $i\pa_tu+Δu=(|\cdot|^{-4}\ast|u|^2)u$ in spatial dimension and prove almost sure scattering with initial data $u_0…