Related papers: Orthonormal Strichartz estimate for dispersive equ…
A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new…
We study the Strichartz estimates for the magnetic Schr\"odinger equation in dimension $n\geq3$. More specifically, for all Schr\"odinger admissible pairs $(r,q)$, we establish the estimate $$ \|e^{itH}f\|_{L^{q}_{t}(\mathbb{R};…
We analyze dynamical properties of the logarithmic Schr{\"o}dinger equation under a quadratic potential. The sign of the nonlinearity is such that it is known that in the absence of external potential, every solution is dispersive, with a…
In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
We analyze the one-dimensional semi-classical Schr\"odinger equation on the half-line with a linear potential and Dirichlet boundary conditions. Our main focus is on establishing improved dispersive and Strichartz estimates for this model,…
We show decay estimates for the propagator of the discrete Schr\"odinger and Klein-Gordon equations in the form $\norm{U(t)f}{l^\infty}\leq C (1+|t|)^{-d/3}\norm{f}{l^1}$. This implies a corresponding (restricted) set of Strichartz…
We study resonances associated to Schr\"odinger operators with compactly supported potentials on ${\mathbb R}^d$, $d\geq3$, odd. We consider compactly supported potentials depending holomorphically on a complex parameter $z$. For certain…
We show trilinear Strichartz estimates in one and two dimensions on frequency-dependent time intervals. These improve on the corresponding linear estimates of periodic solutions to the Schr\"odinger equation. The proof combines decoupling…
For Schr\"{o}dinger equations with potentials which grow at most quadratically at spatial infinity, we prove Strichartz estimates in Wiener amalgam spaces. These estimates provide a stronger recovery of local-in-space regularity than the…
We improve our previous result [L. Molinet and T. Tanaka, Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations, J. Funct. Anal. 283 (2022), 109490] on the Cauchy problem for one dimensional…
We obtain weighted $L^2$ estimates for the elastic wave equation perturbed by singular potentials including the inverse-square potential. We then deduce the Strichartz estimates under the sole ellipticity condition for the Lam\'e operator…
Let $\Delta_{k,a}$ and $\Delta_k $ be the $(k,a)$-generalized Laguerre operator and the Dunkl Laplacian operator on $\mathbb{R}^n$, respectively. The aim of this article is twofold. First, we prove a restriction theorem for the…
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…
This paper investigates maximal estimates of the wave operators for orthonormal families of initial data. We extend the classical maximal estimates for the wave operator by making partial progress on maximal estimates for orthonormal…
We prove dispersive estimates for the low frequency part of the Schrodinger group for a large class of potentials in dimensions greater or equal to four. As a consequence, we extend the result of Journe, Sofer and Sogge to a larger class of…
We study the large-time behavior of global energy class ($H^1$) solutions of the one-dimensional nonlinear Schr\"odinger equation with a general localized potential term and a defocusing nonlinear term. By using a new type of interaction…
We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and Schr\"odinger equations in high dimensions. For the homogeneous estimates, we show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high dimensions by…
In this paper we prove Strichartz estimates for the Dirac equation on asymptotically flat manifolds. The proof combines the weak dispersive estimates proved by the first two authors with the Strichartz and smoothing estimates for the wave…