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Rate of \(L^ 2\)-concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power. (English) Zbl 0726.35124

The author has studied the rate of \(L^ 2\)-concentration for radially symmetric blow-up solutions of the following nonlinear Schrödinger equation with \(f(u)\simeq -| u|^{4/N}u\) as \(| u| \to +\infty\), \[ i\partial u/\partial t=-\Delta u+f(u),\quad t\in [0,T),\quad x\in {\mathbb{R}}^ N;\quad u(0,x)=x_ 0(x),\quad x\in {\mathbb{R}}^ N, \] where \(T>0\) and \(N>2.\)
In Corollary 1.2 there is given a lower estimate of the blow-up order concerning the \(L^ q\) norm of blow-up solutions, \(2<q<+\infty\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B40 Asymptotic behavior of solutions to PDEs
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