Energy equality of weak solutions of the 2D reduced‐gravity two‐and‐a‐half layer system allowing vacuum

Abstract

The energy conservation problem for the reduced‐gravity two‐and‐a‐half layer model remains a challenging open problem, with several recent contributions addressing various aspects of it. In this paper, we establish sufficient conditions on the regularity of weak solutions that guarantee energy conservation even in the presence of a vacuum. Our theorem corresponds to an improvement of some recent results on this problem and contains some well‐known results as a particular case.