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

Qi Zhang

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arXiv · 2109.10423

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

Qi Zhang

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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.

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Qi Zhang. 2021-09-21. Global well-posedness for the nonlinear generalized parabolic Anderson model equation. https://arxiv.org/abs/2109.10423

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