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arXiv · 2407.00722

Global pathwise solutions of an abstract stochastic equation

Y. -X. Lin·Y. -G. Wang
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Abstract

We establish the existence and uniqueness of the maximal pathwise solution for an abstract nonlinear stochastic evolutional equation, which takes the two and three dimensional stochastic Navier-Stokes equations as a typical model, forced by a multiplicative white noise, and show that the pathwise solution exists globally in time in a positive probability when the initial data is sufficiently small. Moreover, a global pathwise solution is obtained for the stochastic Navier-Stokes equations defined on torus when the data is properly regular and small.

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Y. -X. Lin, Y. -G. Wang. 2024-06-30. Global pathwise solutions of an abstract stochastic equation. https://arxiv.org/abs/2407.00722

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