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Global results for a Cauchy problem related to biharmonic wave maps

Tobias Schmid

Vol. 6 (2024), No. 3, 657–691
Abstract

We prove global existence of a derivative biharmonic wave equation with a nongeneric quadratic nonlinearity and small initial data in the scaling critical space

d22,1(d) × d222,1(d)

for d 3. Since the solution persists higher regularity of the initial data, we obtain a small data global regularity result for the biharmonic wave maps equation for a certain class of target manifolds including the sphere.

Keywords
biharmonic map, fourth order, wave maps, Schrödinger maps, Global regularity, lateral Strichartz estimate
Mathematical Subject Classification
Primary: 35A01
Secondary: 35G50
Milestones
Received: 16 September 2022
Revised: 23 May 2024
Accepted: 2 July 2024
Published: 1 October 2024
Authors
Tobias Schmid
École Polytechnique Fédérale de Lausanne
Lausanne
Switzerland