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Global Well-Posedness for the $L^2$-critical nonlinear Schrodinger equation in higher dimensions

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 نشر من قبل Nikolaos Tzirakis
 تاريخ النشر 2006
  مجال البحث
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The initial value problem for the $L^{2}$ critical semilinear Schrodinger equation in $R^n, n geq 3$ is considered. We show that the problem is globally well posed in $H^{s}({Bbb R^{n}})$ when $1>s>frac{sqrt{7}-1}{3}$ for $n=3$, and when $1>s> frac{-(n-2)+sqrt{(n-2)^2+8(n-2)}}{4}$ for $n geq 4$. We use the ``$I$-method combined with a local in time Morawetz estimate.



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