Sharp asymptotic behavior of solutions to Benjamin-Ono type equations-short range case

被引：0

作者：

Kita, Naoyasu ^{[1
]}

Wada, Takeshi ^{[2
]}

机构：

[1] Kumamoto Univ, Fac Adv Sci & Technol, Kumamoto 8608555, Japan

[2] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 497卷 / 02期

关键词：

Benjamin-Ono type equations; Large time behavior; Asymptotic expansion; GLOBAL WELL-POSEDNESS; CAUCHY-PROBLEM; WAVES; IVP;

D O I：

10.1016/j.jmaa.2020.124879

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the large time behavior of a small solution to the generalized Benjamin-Ono equation with a short range nonlinearity, i.e., with the power of nonlinearity greater than 3. In this case, it is well-known that the solution is asymptotically free as t -> infinity. We are interested in the asymptotic expansion of the solution, and determine the second asymptotic term. In order to specify the second asymptotic term, we will apply a technique of Fourier series expansion. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：12

共 27 条

[1] NONLOCAL MODELS FOR NONLINEAR, DISPERSIVE WAVES [J].

ABDELOUHAB, L ;

BONA, JL ;

FELLAND, M ;

SAUT, JC .

PHYSICA D, 1989, 40 (03) :360-392

[2]

Abdelouhab L, 1992, DIFFERENTIAL INTEGRA, V5, P307

[3] INTERNAL WAVES OF PERMANENT FORM IN FLUIDS OF GREAT DEPTH [J].

BENJAMIN, TB .

JOURNAL OF FLUID MECHANICS, 1967, 29 :559-&

[4] On well-posedness for the Benjamin-Ono equation [J].

Burq, Nicolas ;

Planchon, Fabrice .

MATHEMATISCHE ANNALEN, 2008, 340 (03) :497-542

[5] The IVP for the Benjamin-Ono equation in weighted Sobolev spaces II [J].

Fonseca, German ;

Linares, Felipe ;

Ponce, Gustavo .

JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 262 (05) :2031-2049

[6] The IVP for the Benjamin-Ono equation in weighted Sobolev spaces [J].

Fonseca, German ;

Ponce, Gustavo .

JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 260 (02) :436-459

[7] Large time asymptotics of solutions to the generalized Benjamin-Ono equation [J].

Hayashi, N ;

Naumkin, PI .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (01) :109-130

[8]

Hayashi N, 2002, DISCRETE CONT DYN S, V8, P237

[9]

Hayashi Nakao., 1994, Differential Integral Equations, V7, P453

[10] Global well-posedness of the Benjamin-Ono equation in low-regularity spaces [J].

Ionescu, Alexandru D. ;

Kenig, Carlos E. .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 20 (03) :753-798

← 1 2 3 →