Global results for a Cauchy problem related to biharmonic wave maps

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

Ḃ_{d ∕ 2}^{2, 1} (ℝ^{d}) \times Ḃ_{d ∕ 2 - 2}^{2, 1} (ℝ^{d})

for $d \geq 3$ . 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.

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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

Vol. 6, No. 3, 2024

Tobias Schmid

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors