7月15日(木) 15:00 -- 16:00 卓 建宏 (中正大学, 台湾) ``Global and singular solutions to the generalized Proudman-Johnson equation.'' <研究発表要旨> We consider the generalized Proudman?-ohnson equation f_{xxt}+ff_{xxx}= a f_{x}f_{xx}, (x\in R, t>0), and show that there is a class of solutions which exist globally for all parameters a having the form ?(n+3)/(n+1) for n ∈ N, thereby extending a result of Bressan and Constantin (2005). Furthermore, we present new proofs of existence of solutions developing spontaneous singularities and compute the corresponding blow-up rates for a<-1 for the periodic case.