The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
نویسندگان
چکیده
منابع مشابه
Blow up Dynamic and Upper Bound on the Blow up Rate for critical nonlinear Schrödinger Equation
We consider the critical nonlinear Schrödinger equation iut = −∆u − |u| 4 N u with initial condition u(0, x) = u0 in dimension N . For u0 ∈ H1, local existence in time of solutions on an interval [0, T ) is known, and there exists finite time blow up solutions, that is u0 such that limt→T<+∞ |ux(t)|L2 = +∞. This is the smallest power in the nonlinearity for which blow up occurs, and is critical...
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(1.1) (NLS) { iut = −∆u− |u| 4 N u, (t, x) ∈ [0, T )×R u(0, x) = u0(x), u0 : R → C with u0 ∈ H = H(R ) in dimension N ≥ 1. From a result of Ginibre and Velo [7], (1.1) is locally well-posed inH and thus, for u0 ∈ H, there exists 0 < T ≤ +∞ such that u(t) ∈ C([0, T ), H) and either T = +∞ (we say the solution is global) or T < +∞ and then lim supt↑T |∇u(t)|L2 = +∞ (we say the solution blows up i...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2005
ISSN: 0003-486X
DOI: 10.4007/annals.2005.161.157