Talagrand's transportation inequality for SPDEs with locally monotone drifts

Ruinan Li; Xinyu Wang

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arXiv · 2303.06533

Talagrand's transportation inequality for SPDEs with locally monotone drifts

Ruinan Li·Xinyu Wang

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Abstract

The purpose of this paper is twofold. Firstly, we prove transportation inequalities ${\bf T_2}(C)$ on the space of continuous paths with respect to the uniform metric for the law of the solution to a class of non-linear monotone stochastic partial differential equations (SPDEs) driven by the Wiener noise. Furthermore, we also establish the ${\bf T_1}(C)$ property for such SPDEs but with merely locally monotone coefficients, including the stochastic Burgers type equation and stochastic $2$-D Navier-Stokes equation.

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Ruinan Li, Xinyu Wang. 2023-03-12. Talagrand's transportation inequality for SPDEs with locally monotone drifts. https://arxiv.org/abs/2303.06533

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