On global regularity of some bi-rotational Euler flows in R4

Abstract

In this paper, we consider incompressible Euler flows in R4 under bi-rotational symmetry, namely solutions that are invariant under rotations in R4 fixing either the first two or last two axes. With the additional swirl-free assumption, our first main result gives local wellposedness of Yudovich-type solutions, extending the work of Danchin (2007) [9] for axisymmetric flows in R3. The second main result establishes global wellposedness under additional decay conditions near the axes and at infinity. This in particular gives global regularity of C infinity smooth and decaying Euler flows in R4 subject to bi-rotational symmetry without swirl. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.