Related papers: Strichartz estimates for the magnetic Schr\"odinge…
We study the global well-posedness theory for the Schr\"odinger Maps equation. We work in $n+1$ dimensions, for $n \geq 3$, and prove a local well-posedness for small initial data in $\dot{B}^{\frac{n}{2}}_{2,1}$.
We prove global-in-time Strichartz estimates for Schr\"odinger equations with multipole Aharonov--Bohm Hamiltonians on $\mathbb{R}^2$. As intermediate steps, we prove global-in-time local smoothing estimates for multipole Aharonov--Bohm…
We prove dispersive and Strichartz estimates for Schr\"{o}dinger equations on normal real form symmetric spaces. These estimates apply to the well-posedness and scattering for the nonlinear Schr\"{o}dinger equations.
In this paper, we studied the space-time estimates for the solution to the Schr\"odinger equation. By polynomial partitioning, induction arguments, bilinear to linear arguments and broad norm estimates, we set up several maximal estimates…
In this paper we consider magnetic Schr\"odinger operators in R^n, n \ge 3. Under almost optimal conditions on the potentials in terms of decay and regularity we prove smoothing and Strichartz estimates, as well as a limiting absorption…
We establish sharp-in-time kernel and dispersive estimates for the Schr\"odinger equation on non-compact Riemannian symmetric spaces of any rank. Due to the particular geometry at infinity and the Kunze-Stein phenomenon, these properties…
We study the computability of global solutions to linear Schr\"odinger equations with magnetic fields and the Hartree equation on $\mathbb R^3$. We show that the solution can always be globally computed with error control on the entire…
There have been a lot of works concerning the Strichartz estimates for the perturbed Schr\"odinger equation by potential. These can be basically carried out adopting the well-known procedure for obtaining the Strichartz estimates from the…
We are mainly interested in extending the known results on ob-servability inequalities and stabilization for the Schr{\"o}dinger equation to the magnetic Schr{\"o}dinger equation. That is in presence of a magnetic potential. We establish…
We study local-in-time and global-in-time bilinear Strichartz estimates for the Schr\"odinger equation on waveguides. As applications, we apply those estimates to study global well-posedness of nonlinear Schr\"odinger equations on these…
In this paper we prove bilinear Strichartz estimates for a solution to the Schr{\"o}dinger map problem whose size is small in the critical Strichartz space $| |\nabla|^{\frac{d - 2}{2}} \psi_{x} |_{L_{t,x}^{\frac{2(d + 2)}{d}}}$. These…
We study the non-linear Schr\"{o}dinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.
In this paper, we prove new Strichartz estimates for linear Schrodinger equations posed on d-dimensional irrational tori. Then, we use these estimates to prove subcritical and critical local well-posedness results for nonlinear Schrodinger…
We prove Strichartz estimates for the absolutely continuous evolution of a Schr\"odinger operator $H = (i\nabla + A)^2 + V$ in $\R^n$, $n > 2$. Both the magnetic and electric potentials are time-independent and satisfy pointwise polynomial…
The endpoint Strichartz estimates for the Schr\"odinger equation are known to be false in two dimensions. However, if one averages the solution in $L^2$ in the angular variable, we show that the homogeneous endpoint and the retarded…
We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ for solutions to the Schr\"odinger equation on Zoll manifolds, including, in particular, the standard round sphere $S^d$. The proof relies on the arithmetic…
In this paper we generalize the classical Strichartz estimation for solutions of initial problem for linear parabolic and Schr\"odinger PDE on many popular classes {\it pairs} of rearrangement invariant(r.i.) spaces and construct some…
Sharp Strichartz estimates are proved for Schr\"odinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how…
The paper studies existence of ground states for the nonlinear Schr\"odinger equation with a general external magnetic field. In particular, no lattice periodicity or symmetry of the magnetic field, or presence of external electric field is…
We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on the duality principle and the smooth perturbation theory…