Work

Biharmonic wave maps: local wellposedness in high regularity

Year: 2020

Type: article

Abstract: We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave maps equation we use a vanishing viscosity argument and an appropriate parabolic regularization in order to obtain the existence result. The geometric nature of the equation is exploited to prove convergence of approximate solutions, uniqueness of the limit, and continuous dependence on initial data.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ab73ce

Authors: Sebastian Herr, Tobias Lamm, Tobias Schmid, Roland Schnaubelt

Institutions: Bielefeld University, Karlsruhe Institute of Technology

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funder: Deutsche Forschungsgemeinschaft