Related papers: Strichartz estimates for convex co-compact hyperbo…

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global…

We consider an anisotropic model case for a strictly convex domain of dimension $d\geq 2$ with smoothboundary and we describe dispersion forthe semi-classical Schr{\"o}dinger equation with Dirichlet boundary condition. More specifically, we…

We deal with fixed-time and Strichartz estimates for the Schr\"odinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical…

We give several remarks on Strichartz estimates for homogeneous wave equation with special attention to the cases of $L^\infty_x$ estimates, radial solutions and initial data from the inhomogeneous Sobolev spaces. In particular, we give the…

In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domains in real projective space. We also establish a…

We firstly prove Strichartz estimates for the fractional Schr\"odinger equations on $\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We then prove Strichartz estimates for the fractional Schr\"odinger and wave equations on compact…

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…

In this article we prove local well-posedness in low-regularity Sobolev spaces for general quasilinear Schr\"odinger equations. These results represent improvements of the pioneering works by Kenig-Ponce-Vega and Kenig-Ponce-Rolvung-Vega,…

We establish a dispersive estimate (with a decay of 1/t), valid for all times, for the Schroedinger evolution on a non-compact 2-dimensional manifold with a trapped geodesic.

We prove smoothing estimates for velocity averages of the kinetic transport equation in hyperbolic Sobolev spaces at the critical regularity, leading to a complete characterisation of the allowable regularity exponents. Such estimates will…

In this paper, we first give some new characterizations of geodesic spheres in the hyperbolic space by the condition that hypersurface has constant weighted shifted mean curvatures, or constant weighted shifted mean curvature ratio, which…

We study the long time behavior of radial solutions to nonlinear Schr\"{o}dinger equations on hyperbolic space. We show that the usual distinction between short range and long range nonlinearity is modified: the geometry of the hyperbolic…

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…

We prove existence results and lower bounds for the resonances of Schr\"odinger operators associated to smooth, compactly support potentials on hyperbolic space. The results are derived from a combination of heat and wave trace expansions…

We show Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients via $\ell^2$-decoupling. When we additionally average in time, further improvements can be obtained. Next, we apply multilinear refinements to show…

In this paper, we investigate Strichartz estimates for discrete linear Schr\"odinger and discrete linear Klein-Gordon equations on a lattice $h\mathbb{Z}^d$ with $h>0$, where $h$ is the distance between two adjacent lattice points. As for…

We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss…

New Strichartz estimates for the modulated cubic nonlinear Schr\"{o}dinger equation are proved. These Strichartz estimates allow us to show that this equation is pathwise locally well-posed. We also show that improved Strichartz estimates…

We prove Strichatz inequalities for the Schr{\"o}dinger equation and the wave equation with multiplicative noise on a two-dimensional manifold. This relies on the Anderson Hamiltonian H described using high order paracontrolled calculus. As…

We establish Strichartz estimates for the Schr\"odinger equation on Riemannian manifolds $(\Omega,\g)$ with boundary, for both the compact case and the case that $\Omega$ is the exterior of a smooth, non-trapping obstacle in Euclidean…