Global well-posedness for the nonlinear generalized parabolic Anderson model equation

Abstract

We study the global existence of the singular nonlinear parabolic Anderson model equation on $2$-dimensional tours ${\mathbb{T}}^2$. The method is based on paracontrolled distribution and renormalization. After split the original nonlinear parabolic Anderson model equation into two simple equations, we prove the global well-posedness by some a priori estimates and smooth approximations. Furthermore, we prove the uniqueness of the solution by using classical energy estimates.

References in corpus (4)

• A simple construction of the continuum parabolic Anderson model on ${\mathbf{R}}^2$
• The continuous Anderson hamiltonian in dimension two
• The continuous Anderson hamiltonian in $d\le 3$
• Stochastic Heat Equation with general noise

Cited by in corpus (1)

• Constraint Minimization Problem of the Nonlinear Schrödinger Equation with the Anderson Hamiltonian