Local and global well-posedness for the Ostrovsky equation

We consider the initial value problem for where u is a real valued function, β and γ are real numbers such that β•γ≠0 and . This equation differs from Korteweg–de Vries equation in a nonlocal term. Nevertheless, we obtained local well-posedness in , , using techniques developed in [C.E. Kenig, G. Ponce, L. Vega, Well-posedness of the initial value problem for the Korteweg–de Vries equation, J. Amer. Math. Soc. 4 (1991) 323–347]. For the case β•γ>0, we also obtain a global result in X1, using appropriate conservation laws.