Global well‐posedness of inviscid lake equations in the Besov spaces

Abstract

In this paper, we make the first attempt to investigate the Cauchy problem of a shallow water model, namely, the inviscid lake equations, in the Besov spaces.Notably, we prove the global existence and uniqueness of the solutions in the Besov spaces B s p,q (R 2 ) for s > 2 p + 1 and s = 2 p + 1 if q = 1, which contain the particular case of the endpoint Besov space B 1 ∞,1 (R 2 ).