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

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 Bp,qs(Double-struck capital R2)$$ {B}_{p,q} circumflex s\left({\mathbb{R}} circumflex 2\right) $$ for s>2p+1$$ s >\frac{2}{p}+1 $$ and s=2p+1$$ s equal to \frac{2}{p}+1 $$ if q=1$$ q equal to 1 $$, which contain the particular case of the endpoint Besov space B infinity,11(Double-struck capital R2)$$ {B}_{\infty, 1} circumflex 1\left({\mathbb{R}} circumflex 2\right) $$.