In this paper, we prove global well-posedness and scattering below the energy space for the defocusing nonlinear Schr\"odinger equation with intercritical power nonlinearities in spatial dimensions $d\geq3$, improving the regularity threshold of Vi\c{s}an and Zhang [Differ. Integr. Equations, 22(2009), 99-124].
Zu-Yu Ma, Changxing Miao, Yi-Lin Song et al.· 0 citations
In this paper, we study the focusing mass-critical Hartree equation \[ iu_t+\Delta u=-\bigl(|x|^{-2}*|u|^2\bigr)u \] at the ground-state mass $M(Q)$. We prove that, up to the symmetries of the equation, every global minimal-mass non-scattering solution is a solitary wave, while every finite-time minimal-mass blowup sol...
In this paper, we prove that the defocusing mass-critical Hartree equation is global well-posed and scatters for any initial data $u_0\in L^2$, and prove the analogous result in the focusing case, provided the mass of $u_0$ is strictly less than that of the ground state $Q$. This result removes the radial restriction f...
Zu-Yu Ma, Changxing Miao, Matthew Rosenzweig et al.· 1 citation· ⚡1
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