On Stability of Pseudo-conformal Blowup for L-critical Hartree Nls
نویسنده
چکیده
We consider L-critical focusing nonlinear Schrödinger equations with Hartree type nonlinearity i∂tu = −∆u− ` Φ ∗ |u| ́ u in R, where Φ(x) is a perturbation of the convolution kernel |x|. Despite the lack of pseudo-conformal invariance for this equation, we prove the existence of critical mass finite-time blowup solutions u(t, x) that exhibit the pseudoconformal blowup rate L2x ∼ 1 |t| as t ր 0. Furthermore, we prove the finite-codimensional stability of this conformal blow up, by extending the nonlinear wave operator construction by Bourgain and Wang (see [BW97]) to L-critical Hartree NLS.
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