Type: Article

Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

Bernal-Vílchis, Fernando; Nakao, Hayashi; Naumkin, Pavel I;

Abstract:

We consider the Cauchy problem for the Ostrovsky-Hunter equation ?x(?tu?(b/3)?3xu??xKu3)=au, (t,x)?R2, u(0,x)=u0(x), x?R, where ab>0. Define ?0=(27a/b)1/4. Suppose that K is a pseudodifferential operator with a symbol K^(?) such that K^(±?0)=0, ImK^(?)=0, and |K^(?)|?C. For example, we can take K^(?)=(?2??20)/(?2+1). We prove the global in time existence and the large time asymptotic behavior of solutions.