Large Time Asymptotics for the Reduced Ostrovsky Equation

Abstract

We consider the Cauchy problem for the reduced Ostrovsky equation $$u_{tx} = u + \left(u^{3}\right)_{xx}$$ with real valued initial data \({u \left(0\right) = u_{0}}\). 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.