Optimal L2-growth of the generalized Rosenau equation

被引：0

作者：

Li, Xiaoyan ^{[1
]}

Ikehata, Ryo ^{[2
]}

机构：

[1] Hainan Univ, Sch Math & Stat, Haikou 570228, Hainan, Peoples R China

[2] Hiroshima Univ, Grad Sch Humanities & Social Sci, Dept Math, Div Educ Sci, Higashihiroshima 7398524, Japan

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2024年 / 15卷 / 03期

关键词：

Rosenau equation; Fourier analysis; Weighted L-1-data; Low dimensional case; Growth estimates; WAVE-EQUATIONS; ASYMPTOTIC PROFILES; PLATE EQUATION; CAUCHY-PROBLEM; DECAY-RATES; INEQUALITIES; EXISTENCE; DYNAMICS; BEHAVIOR;

D O I：

10.1007/s11868-024-00635-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We report that the quantity measured in the L-2 norm of the solution itself of the generalized Rosenau equation, which was completely unknown in this equation, grows in the proper order at time infinity. It is also immediately apparent that this growth aspect does not occur in three or more spatial dimensions, so we will apply the results obtained in this study to provide another proof that Hardy-type inequalities do not hold in the case of one or two spatial dimensions.

引用

页数：28

共 50 条

[41] FILTERING THE L2 CRITICAL FOCUSING SCHRODINGER EQUATION
Sun, Ruoci
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (10) : 5973 - 5990
[42] An Inhomogeneous, L2-Critical, Nonlinear Schrodinger Equation
Genoud, Francois
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2012, 31 (03): : 283 - 290
[43] Two Solutions for the Planar Generalized Quasilinear Schrödinger Equation with Combined Nonlinearities and Critical Exponential Growth
Zhao, Wenting
Huang, Xianjiu
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2025, 51 (02)
[44] MULTIPLICITY OF SOLUTIONS FOR A GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION WITH POTENTIAL IN R2
Xie, Zheng
Chen, Jing
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 2023 (48) : 1 - 17
[45] Blow-Up Analysis of L2-Norm Solutions for an Elliptic Equation with a Varying Nonlocal Term
Zhu, Xincai
He, Chunxia
AXIOMS, 2024, 13 (05)
[46] Lump and interactional solutions of the (2+1)-dimensional generalized breaking soliton equation
Fan, Yu-Pei
Chen, Ai-Hua
MODERN PHYSICS LETTERS B, 2020, 34 (03):
[47] ON THE L2-CRITICAL NONLINEAR SCHRODINGER EQUATION WITH A NONLINEAR DAMPING
Darwich, Mohamad
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (06) : 2377 - 2394
[48] Vortex collapse for the L2-critical nonlinear Schrodinger equation
Simpson, G.
Zwiers, I.
JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (08)
[49] On singularity formation for the L2-critical Boson star equation
Lenzmann, Enno
Lewin, Mathieu
NONLINEARITY, 2011, 24 (12) : 3515 - 3540
[50] Normalized solutions for Kirchhoff equation with L2-critical exponents
Liu, Changlin
Lv, Ying
Ou, Zengqi
JOURNAL OF MATHEMATICAL PHYSICS, 2024, 65 (07)

← 1 2 3 4 5 →