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...
A uniform magnetic field completely suppresses long-time dispersion for the Euclidean Landau Hamiltonian. We show that negative curvature fundamentally changes this behavior. For the Landau Hamiltonian with arbitrary field strength $B\in\mathbb R$ on the hyperbolic plane $\mathbb H$, we establish sharp dispersive estim...
Huan-Qing Guo, Hao-Ran Wang, Jun-Yong Zhang et al.· 0 citations
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
We consider the three-dimensional defocusing cubic nonlinear Schr\"odinger equation with variable coefficients, a magnetic potential, and a non-negative localized damping term, \[ i\partial_tu+(\nabla-iA)\cdot G(\nabla-iA)u+ia(x)u=|u|^2u, \qquad t>0,\quad x\in\mathbb R^3. \] No non-trapping condition is imposed on the...
Luca Fanelli, Haruya Mizutani, Yi-Lin Song et al.· 0 citations
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