Strichartz estimate for wave equation
WebFeb 5, 2015 · Blair, Ford and Marzuola established global Strichartz estimates for the wave equation on flat cones C (S ρ 1) by using the explicit representation of the fundamental … WebIn this paper we are interested in improved Strichartz estimates for systems of inhomogeneous wave and Schrodinger equations, when the inhomogeneity is a divergence free vector field at any given time. The starting point is the following simple observation: Proposition 1. Suppose u 1+2 → 2 is a (weak) solution of the following system of wave ...
Strichartz estimate for wave equation
Did you know?
WebThe idea consists in squaring equation (1) in order to obtain a system of wave or Klein-Gordon equations on the manifold pM, gq (depending on whether m “ 0 or m ą 0), and then combining the estimates for such flows on asymptotically flat manifolds with the standard argument based on Duhamel formula and local smoothing estimates to control ... Webarising in the study of quasilinear wave equations, see [9]. The result we prove here is stronger, since a classical argument shows that the dispersive estimates (4) imply the Strichartz estimates (5). In-terestingly enough, the range of pthat we can allow in Theorem 1.1 is exactly the range which is needed in order to prove the dispersive esti-
WebStrichartz estimates for the Dunkl wave equation and application Hatem Mejjaoli Department of Mathematics, Faculty of Sciences of Tunis, CAMPUS, 1060 Tunis, Tunisia a … WebApr 12, 2024 · We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n 4) and the …
WebMay 31, 2014 · We calculate the the sharp constant and characterize the extremal initial data in H ˙ 3 4 × H ˙ − 1 4 for the L 4 Sobolev--Strichartz estimate for the wave equation in four spatial dimensions. Keywords: Strichartz estimates, wave equation, sharp constants. Mathematics Subject Classification: Primary 35B45; Secondary 35L05. Citation: Related … WebWe are also obtain improved endpoint Strichartz estimates for manifolds of nonpositive curvature, which cannot hold for spheres. We obtain improved Strichartz estimates for …
WebIn this note we consider a strictly convex domain Ω ⊂ ℝ d of dimension d ≥ 2 with smooth boundary ∂ Ω ≠ ∅ and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the …
WebIn mathematical analysis, Strichartz estimatesare a family of inequalities for linear dispersive partial differential equations. These inequalities establish size and decay of … old swan furniture shopWebIn this paper we shall prove a Strichartz estimate in the following abstract setting (see below for the concrete examples of the wave and Schr¨odinger equation): let (X,dx) be a … old swan gargrave fireWebarXiv:math/0404011v2 [math.AP] 23 Dec 2004 MAXIMIZERS FOR THE STRICHARTZ INEQUALITY DAMIANO FOSCHI Dipartimento di Matematica Pura e Applicata Universit`a … is a bunny a producerWeb1. Schrodinger vs. wave equations We now turn to the analogous Strichartz estimates for the wave equation. When we proved them for the Schr odinger equation the key estimate was the decay estimate (1.1) sup x2Rn j(eit h)(x)j (4ˇjtj) n2khk 1: In Assignment #6, you considered an analogous estimate for the wave equation @2 tu u= 0 with initial ... old swan gargrave facebookWebWe analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint … is a bunny a primary consumerWebWe are also obtain improved endpoint Strichartz estimates for manifolds of nonpositive curvature, which cannot hold for spheres. We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on negatively curved compact manifolds which improve the classical universal results results of Burq, G\'erard and Tzvetkov [11] in ... old swan group practiceWebStrichartz estimates are spacetime estimates on homogeneous and inhomogeneous linear dispersive and wave equations. They are particularly useful for solving semilinear … old swan gas services