Type: Article

Large time asymptotics for the reduced Ostrovsky equation

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

We consider the Cauchy problem for the reduced Ostrovsky equation utx=u+(u3)xx with real valued initial data u(0)=u0 . We introduce the factorization for the free evolution group to prove the global existence of solutions. Also, we show that the large time asymptotics of solutions has a logarithmic correction in the phase comparing with the corresponding linear case.