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.