Web1. 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 ... WebSep 1, 2009 · Strichartz estimates are a family of space time integra- lity estimates on solutions u (t, x) : (−T ,T )×M→C to the wave equation ∂2t u (t, x)− gu (t, x)= 0, u (0, x)= f (x), ∂tu (0, x)= g (x), (1.1) here g denotes the Laplace–Beltrami operator on (M,g).
Dispersive estimates for nonhomogeneous radial phases
WebOn Strichartz estimate for many body Schr\"odinger equation in the waveguide setting @inproceedings{Zhao2024OnSE, title={On Strichartz estimate for many body … 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 … celery testosterone
Virial identity and weak dispersion for the magnetic Dirac equation
Weballows us to prove Strichartz type estimates for the wave equation with nonsmooth co-efficients. Finally, we use these Strichartz estimates to improve the local theory for second order nonlinear hyperbolic equations. 1 Introduction The FBI transform is, in a way, similar to the complex Fourier transform, in that for each Websolution of the wave equation on R3+1 plays an important role in these arguments. Consequently, a new idea was needed if one wanted to generalize these results to higher dimensions. The missing link, apparently, was the Strichartz estimate. Its importance for nonlinear wave equations in higher dimensions had long been 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 … celery tesco