Cauchy problem of Schrodinger-Improved Boussinesq Systems on the torus

被引：2

作者：

Zhong, Sijia ^{[1
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 415卷 / 01期

关键词：

Schrodinger-Improved Boussinesq; System; Local well-posedness; Global well-posedness; Noise; DE-VRIES EQUATION; ZAKHAROV SYSTEM; WELL-POSEDNESS; WHITE-NOISE; DRIVEN;

D O I：

10.1016/j.jmaa.2014.01.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will study the local well-posedness of Schrodinger-Improved Boussinesq System with additive noise in T-d, d >= 1, and we will also study the global well-posedness of dimension 1 case with the initial data (u(0), v(1), v(2)) is an element of L-2 x L-2 x L-2 almost surely, gaining some exponential growth of L-2 norm of v. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：217 / 239

页数：23

共 18 条

[1] Well-posedness for the Schrodinger-improved Boussinesq system and related bilinear estimates [J].

Akahori, Takafumi .

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2007, 50 (03) :469-489

[2] On the 2D Zakharov system with L2 Schrodinger data [J].

Bejenaru, I. ;

Herr, S. ;

Holmer, J. ;

Tataru, D. .

NONLINEARITY, 2009, 22 (05) :1063-1089

[3] Convolutions of singular measures and applications to the Zakharov system [J].

Bejenaru, Ioan ;

Herr, Sebastian .

JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 261 (02) :478-506

[4]

Bourgain J., 1999, Amer. Math. Soc. Colloq. Publ., V46

[5] Bilinear eigenfunction estimates and the nonlinear Schrodinger equation on surfaces [J].

Burq, N ;

Gérard, P ;

Tzvetkov, N .

INVENTIONES MATHEMATICAE, 2005, 159 (01) :187-223

[6] Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrodinger systems [J].

Colliander, James ;

Holmer, Justin ;

Tzirakis, Nikolaos .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 360 (09) :4619-4638

[7]

Da Prato G., 1992, Encyclopedia Math. Appl.

[8] Periodic solutions of the Korteweg-de Vries equation driven by white noise [J].

De Bouard, A ;

Debussche, A ;

Tsutsumi, Y .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2004, 36 (03) :815-855

[9] The stochastic nonlinear Schrodinger equation in H 1 [J].

de Bouard, A ;

Debussche, A .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (01) :97-126

[10] White noise driven Korteweg-de Vries equation [J].

de Bouard, A ;

Debussche, A ;

Tsutsumi, Y .

JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 169 (02) :532-558

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