二维空间中一类广义Zakharov系统爆破率的下界估计

Lower Bounds of the Blowup Rate for a Kind of Generalized Zakharov System in Dimension Two

研究二维空间中一类广义Zakharov系统{iE_(1)t+ΔE_(1)-nE_(1)+E_(2)(E_(1)E_(2)-E_(1)E_(2))=0,iE_(2)t+ΔE_(2)-nE_(2)+E_(1)(E_(1)E_(2)-E_(1)E_(2))=0,nt=-·v,vt=-n-(|E_(1)|^(2)+|E_(2)|^(2))的初值问题.利用时空尺度变换及算子半群理论,得到其有限时间爆破解(E_(1),E_(2),n,v)(t)的爆破率的一个下界估计,即当t→T(有限爆破时间)时,存在仅依赖于初始值的常数c>0,使得‖(E_(1),E_(2),n,v)‖H 1(R^(2))×H 1(R^(2))×L^(2)(R^(2))×L^(2)(R^(2))≥c/T-√t.

In this paper,we study the initial value problem for a kind of generalized Zakharov system in dimension two:■.Using space-time scaling transform and the theory of operator semigroup,we obtain a lower bound of the blowup rate for the finite time blowup solution(E1,E2,n,v)( t) to the Cauchy problem under consideration. That is,for t near T(blowup time),there exists some c>0 relying only on initial data such that■ .