Stochastic continuity equation with non-smooth velocity
David A.C., Christian Olivera
TL;DR
This paper investigates the existence and uniqueness of solutions to the stochastic continuity equation when the velocity field has irregular, non-smooth coefficients, addressing challenges in stochastic PDEs with rough data.
Contribution
It establishes conditions for existence and uniqueness of solutions to stochastic continuity equations with non-smooth velocity fields, advancing understanding of stochastic PDEs with irregular coefficients.
Findings
Proved existence of solutions under irregular velocity conditions
Established uniqueness results for non-smooth coefficients
Extended stochastic PDE theory to rough coefficient scenarios
Abstract
In this article we study the existence and uniqueness of solutions of stochastic continuity equation with irregular coefficients.
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Taxonomy
TopicsNavier-Stokes equation solutions · Stochastic processes and financial applications · Stability and Controllability of Differential Equations