Regularization by Noise in One-Dimensional Continuity Equation

被引：5

作者：

Olivera, Christian ^{[1
]}

机构：

[1] Univ Estadual Campinas, Dept Matemat, Campinas, SP, Brazil

来源：

POTENTIAL ANALYSIS | 2019年 / 51卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Stochastic partial differential equation; Continuity equation; Regularization by noise; Ito-Wentzell-Kunita formula; Low regularity; SCALAR CONSERVATION-LAWS; TRANSPORT-EQUATIONS; DIFFERENTIAL-EQUATIONS; FLOWS;

D O I：

10.1007/s11118-018-9700-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：23 / 35

页数：13

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