Global weak solutions to the Novikov equation by viscous approximation

被引：1
|
作者：
Zheng, Rudong [1 ]
Yin, Zhaoyang [2 ,3 ]
Guo, Boling [4 ]
机构：
[1] Guangdong Univ Technol, Sch Math & Stat, Guangzhou 510520, Peoples R China
[2] Sun Yat sen Univ, Dept Math, Guangzhou 510275, Peoples R China
[3] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China
[4] Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2023年 / 70卷
关键词：
Novikov equation; Vanishing viscosity; Weak solutions; Peakon; VARIATIONAL WAVE-EQUATION; SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; CONSERVATIVE SOLUTIONS; DISSIPATIVE SOLUTIONS; WELL-POSEDNESS; CAUCHY-PROBLEM; ILL-POSEDNESS; BLOW-UP; EXISTENCE;
D O I：
10.1016/j.nonrwa.2022.103767
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study global weak solutions to the Novikov equation by vanishing viscosity method. We prove that global weak solutions can be obtained as weak limits of viscous approximations for a class of initial data. The proof relies on a space-time higher integrability estimate and the method of renormalization. In addition, we analyze the interaction of peakon and antipeakon and prove that wave breaking leads to energy concentration. By different continuations beyond the wave breaking, we obtain conservative solutions and dissipative solutions respectively.(c) 2022 Elsevier Ltd. All rights reserved.
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页数：20
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