Research on propagation of singularities for nonlinear wave equations

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1.The head investigator and co-investigator T.Ogawa has studied on the sufficient condition for solutions to the Benjamin-Ono equation to be analytic in space and time variables for t>0 with E.Kaikina and P.I.Naumkin. Under the condition that initial data have some singularity at the origin, we show that the solution is analytic for t>0.2.We have investigated the existence of solutions for the initial value problem of the Benjamin-Ono equation. However it is impossible to apply Picard's iteration method to the Benjamin-Ono equation in usual Sobolev space, we show that Picard's iteration method is applicable for some Sobolev space with homogeneous and inhomogeneous multipliers.3.We have investigate the propagation of singularities for the nonlinear wave equations with nonlinear term satisfying null condition. Regularity estimate can be improved under the null condition for nonlinear term.