Some remarks on Strichartz estimates for homogeneous wave equation

Some Remarks on Strichartz Estimates for Homogeneous Wave Equation

In this paper, we give several remarks on Strichartz estimates for homogeneous wave equation. In particular, we show that the endpoint L4t L ∞ x estimate fail to be hold for n = 2 in general. When the data is radial, we prove the endpoint L2t L ∞ x estimate for n ≥ 3, and the L q tL ∞ x estimate with 2 < q < ∞ for n = 2.

Characteristic Strichartz Estimates for the Wave Equation

Strichartz estimates for the wave equation on Riemannian symmetric manifolds

We prove Strichartz type estimates for solutions of the homogeneous wave equation on Riemannian symmetric spaces. Our results generalize those of Ginibre and Velo in [7].

Strichartz Estimates for the Wave Equation on Manifolds with Boundary

Strichartz estimates are well established on flat Euclidean space, where M = R and gij = δij . In that case, one can obtain a global estimate with T = ∞; see for example Strichartz [27], Ginibre and Velo [9], Lindblad and Sogge [16], Keel and Tao [14], and references therein. However, for general manifolds phenomena such as trapped geodesics and finiteness of volume can preclude the development...

Strichartz Estimates for the Wave Equation on Flat Cones

We consider the solution operator for the wave equation on the flat Euclidean cone over the circle of radius ρ > 0, the manifold R+ × ( R / 2πρZ ) equipped with the metric g(r, θ) = dr2 + r2 dθ2. Using explicit representations of the solution operator in regions related to flat wave propagation and diffraction by the cone point, we prove dispersive estimates and hence scale invariant Strichartz...