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| In this talk, we will consider the finite time blowup for the mass-critical focusing NLS of fourth order: $$
iu_t = \Delta^2 u - |x|^{-2}|u|^\frac4n u,\;\;n \ge 5.
$$
The model of inhomogeneous term of nonlinearity is known as the laser beam in Kerr media affected by electrons. The equation is mass-critical in the scaling and satisfies the mass and energy conservation laws. The main ingredient of this talk is to show the fiite time blowup of this equation. We adopt Glassey's virial argument. For this purpose we assume the radial symmetry of solutions, finite fourth moment within the existence time and negative energy. |
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