THE EXISTENCE AND DECAY ESTIMATES OF THE SOLUTIONS TO 3D STOCHASTIC NAVIER-STOKES EQUATIONS WITH ADDITIVE NOISE IN AN EXTERIOR DOMAIN

被引：0
|
作者：
Taniguchi, Takeshi [1 ]
机构：
[1] Kurume Univ, Grad Sch Comparat Culture, Div Math Sci, Kurume, Fukuoka 8398502, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 10期
基金：
日本学术振兴会;
关键词：
Stochastic Navier-Stokes equations; Additive noise; Strong solutions; Exterior domain; Asymptotic behavior of solutions; INITIAL-VALUE PROBLEM; EXPONENTIAL BEHAVIOR;
D O I：
10.3934/dcds.2014.34.4323
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the local existence and global existence with probability 1 sigma (0 < sigma < 1) of pathwise solutions to the threedimensional stochastic Navier-Stokes equation perturbed by a cylindrical Wiener processe W(t) in an exteriour domain: dX(t) = [-AX(t) + B (X(t)) + f(*)(t)]dt + Phi(t)dW(t), where A = -P Delta is the Stokes operator, and f(*)(t) and Phi(t) satisfy some conditions. We also consider the decay of pathwise solutions.
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页码：4323 / 4341
页数：19
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