Related papers: Fractal Strichartz estimate for the wave equation
We consider the sharp Strichartz estimate for the wave equation on $\mathbb R^{1+5}$ in the energy space, due to Bez and Rogers. We show that it can be refined by adding a term proportional to the distance from the set of maximisers, in the…
This note is concerned with Strichartz estimates for the wave equation and orthonormal families of initial data. We provide a survey of the known results and present what seems to be a reasonable conjecture regarding the cases which have…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
We prove sharper Strichartz estimates than expected from theoptimal dispersion bounds.
We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the $L^4_{t,x}(\R^{5+1})$ norm of the solution in terms of the energy. We also characterise the…
We calculate the the sharp constant and characterise the extremal initial data in $\dot{H}^{\frac{3}{4}}\times\dot{H}^{-\frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four space dimensions.
Some analogues of the Schr\"odinger refined Strichartz inequalities (Du, Guth, Li and Zhang) are obtained for the wave equation. These are used to improve the best known $L^2$ fractal Strichartz inequalities for the wave equation in…
In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.
We consider the wave equation with Dirichlet boundary conditions in the exterior of a cylinder in R 3 and we construct a global in time parametrix to derive sharp dispersion estimates for all frequencies (low and high) and, as a corollary,…
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…
We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by…
In this paper we show a general Strichartz estimate for certain perturbed wave equation, and here we can drop the nontrapping hypothesis and handle trapping obstacles with some loss of derivatives for data in the local energy decay…
We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is…
We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…
We prove Strichartz estimates for gravity water waves, in arbitrary dimension and in fluid domains with general bottoms. We consider rough solutions such that, initially, the first order derivatives of the velocity field are not controlled…
We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…
We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by…
Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales…
We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix…
We establish Strichartz estimates (both reversed and some direct ones), pointwise decay estimates, and weighted decay estimates for the linear wave equation in dimension two with an almost scaling-critical potential, in the case when there…