Work

Uniqueness of dissipative solutions for the Camassa–Holm equation

Year: 2024

Type: article

Abstract: We show that the Cauchy problem for the Camassa–Holm equation has a unique, global, weak, and dissipative solution for any initial data u 0 ∈ H 1 ( R ) , such that u 0 , x is bounded from above almost everywhere. In particular, we establish a one-to-one correspondence between the properties specific to the dissipative solutions and a solution operator associating to each initial data exactly one solution.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2024.08.036

Author: Katrin Grunert

Institution: Norwegian University of Science and Technology

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,050

Funders: Swedish Foundation for MS Research, Vetenskapsrådet, Norges Forskningsråd, Cambridge-MIT Institute