Backward stochastic differential equations associated with the vorticity equations

被引：5

作者：

Cruzeiro, A. B. ^{[1
,2
]}

Qian, Z. M. ^{[3
]}

机构：

[1] Univ Lisbon, Grp Fis Matemat, P-1649003 Lisbon, Portugal

[2] Univ Lisbon, Inst Super Tecn, P-1049001 Lisbon, Portugal

[3] Univ Oxford, Math Inst, Oxford OX1 3LB, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 267卷 / 03期

关键词：

Navier-Stokes; Vorticity equations; Backward SDE; GENERAL BOUNDARY CONDITIONS; QUADRATIC GROWTH;

D O I：

10.1016/j.jfa.2014.05.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we derive a non-linear version of the Feynman-Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence (global in time) and uniqueness for a stochastic terminal value problem associated with the vorticity equation in dimension 2. A particular class of terminal values provide, via these probabilistic methods, solutions for the vorticity equation. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：660 / 677

页数：18

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