Regularization by Noise in One-Dimensional Continuity Equation
Potential Analysis(2018)
摘要
A linear stochastic continuity equation with non-regular coefficients is considered. We prove existence and uniqueness of strong solution, in the probabilistic sense, to the Cauchy problem when the vector field has low regularity, in which the classical DiPerna-Lions-Ambrosio theory of uniqueness of distributional solutions does not apply. We solve partially the open problem that is the case when the vector-field has random dependence. In addition, we prove a stability result for the solutions.
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关键词
Stochastic partial differential equation,Continuity equation,Regularization by noise,Itô-Wentzell-Kunita formula,Low regularity
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