LOCAL SOLVABILITY OF THE CAUCHY PROBLEM OF A FIFTH-ORDER NONLINEAR DISPERSIVE EQUATION

摘要

The solvability of the fifth-order nonlinear dispersive equation (partial deriv)_t u + αu((partial deriv)_xu)~2 + β(partial deriv)_x~3u + γ(partial deriv)_x~5u = 0 is studied. By using the approach of Kenig, Ponce and Vega and some Strichartz estimates for the corresponding linear problem, it is proved that if the initial function u_0 belongs to H~s (R) and s > 1/4,then the Cauchy problem has a unique solution in C([ - T,T],H~s (R)) for some T > 0.