MARTINGALE AND PATHWISE SOLUTIONS TO THE STOCHASTIC ZAKHAROV-KUZNETSOV EQUATION WITH MULTIPLICATIVE NOISE

被引：7

作者：

Glatt-Holtz, Nathan ^{[1
]}

Temam, Roger ^{[2
,3
]}

Wang, Chuntian ^{[2
,3
]}

机构：

[1] Virginia Polytech Inst & State Univ, Dept Math, Blacksburg, VA 24061 USA

[2] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[3] Indiana Univ, Inst Sci Comp & Appl Math, Bloomington, IN 47405 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2014年 / 19卷 / 04期

基金：

美国国家科学基金会;

关键词：

Zakharov-Kuznetsov equation; Korteweg-de Vries equation; stochastic fluid dynamics;

D O I：

10.3934/dcdsb.2014.19.1047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed to deal with a special type of boundary conditions and to verify the pathwise uniqueness of martingale solutions with a lack of regularity, where both difficulties arise due to the partly hyperbolic feature of the model.

引用

页码：1047 / 1085

页数：39

共 32 条

[1]

[Anonymous], 1983, Fluid Dynamics in Astrophysics and Geophysics

[2]

Baykova ES, 2013, ADV DIFFERENTIAL EQU, V18, P663

[3] STOCHASTIC NAVIER-STOKES EQUATIONS [J].

BENSOUSSAN, A .

ACTA APPLICANDAE MATHEMATICAE, 1995, 38 (03) :267-304

[4]

Billingsley Patrick, 1995, Probability and Measure

[5] AN EVALUATION OF A MODEL EQUATION FOR WATER-WAVES [J].

BONA, JL ;

PRITCHARD, WG ;

SCOTT, LR .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1981, 302 (1471) :457-510

[6]

Da Prato G., 1992, STOCHASTIC EQUATIONS, DOI 10.1017/CBO9780511666223

[7]

de Bouard A., 2009, ECOLE POLYTECH EXP

[8] Effect of a localized random forcing term on the Korteweg-de Vries equation [J].

Debussche, A ;

Printems, J .

JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2001, 3 (03) :183-206

[9] Local martingale and pathwise solutions for an abstract fluids model [J].

Debussche, Arnaud ;

Glatt-Holtz, Nathan ;

Temam, Roger .

PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (14-15) :1123-1144

[10] Exponential decay for the linear Zakharov-Kuznetsov equation without critical domain restrictions [J].

Doronin, G. G. ;

Larkin, N. A. .

APPLIED MATHEMATICS LETTERS, 2014, 27 :6-10

← 1 2 3 4 →