Strichartz estimate for wave equation

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August undefined, 2024

Webparticular when θ = 0, these estimates corresponding to wave equation serve as a tool for existence results about the nonlinear wave equation. For example, Lindblad– Sogge [32] answered the problem of ﬁnding minimal regularity conditions on the initial data ensuring local well-posedness for semilinear wave equations. Analogous WebJan 4, 2004 · Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay. We prove weighted L^2 (Morawetz) estimates for the solutions of linear …

MAXIMIZERS FOR THE STRICHARTZ INEQUALITY …

WebFeb 12, 2024 · I am a student planning to learn some knowledge about Strichartz estimates for wave equations. My goal is to understand the Strichartz estimates or a priori estiamtes of weak solutions for the linear wave equation as follows \begin{eqnarray} \partial_t^2u-\operatorname{div}(A(x)\nabla u)=0, \end{eqnarray} where $ … WebJan 26, 2009 · Strichartz estimates for the magnetic Schrödinger equation with potentials V of critical decay Seonghak Kim, Youngwoo Koh Mathematics 2016 ABSTRACT We study the Strichartz estimates for the magnetic Schrödinger equation in dimension n≥3. More specifically, for all Schrödinger admissible pairs (r,q), we establish the estimate when … gb18388

Strichartz Estimate and Nonlinear Klein–Gordon Equation on …

WebOn Strichartz estimate for many body Schr\"odinger equation in the waveguide setting @inproceedings{Zhao2024OnSE, title={On Strichartz estimate for many body … WebWe are also obtain improved endpoint Strichartz estimates for manifolds of nonpositive curvature, which cannot hold for spheres. We obtain improved Strichartz estimates for … gb18380道客巴巴

Dispersive and Strichartz estimates for the wave equation in …

Strichartz estimates for the wave and Schrödinger equations with the ...

WebThe global Minkowski Strichartz estimate (1.3) is a generalization of the work of Strichartz [30, 31]. The local Strichartz estimates (1.2) for solutions to the ho-mogeneous (F = 0) … 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- gb18387WebApr 12, 2024 · Abstract: We study linear dispersive equations in dimension one and two for a class of radial nonhomogeneous phases. L 1 $\rightarrow$ L $\infty$ type estimates, Strichartz estimates, local Kato smoothing and Morawetz type estimates are provided. We then apply our results to different water wave models. gb18382

"WebarXiv:math/0404011v2 [math.AP] 23 Dec 2004 MAXIMIZERS FOR THE STRICHARTZ INEQUALITY DAMIANO FOSCHI Dipartimento di Matematica Pura e Applicata Universit`a … " - Strichartz estimate for wave equation

Strichartz estimate for wave equation

How to learn Strichartz estimates for wave equations?

WebStrichartz estimates for the Dunkl wave equation and application Hatem Mejjaoli Department of Mathematics, Faculty of Sciences of Tunis, CAMPUS, 1060 Tunis, Tunisia a … 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

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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 Schrodinger equation (in dimension n 3). WebAug 8, 2024 · Strichartz estimates for the wave equation on a 2d model convex domain. Oana Ivanovici, Gilles Lebeau, Fabrice Planchon. We prove better Strichartz type …

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 WebIn this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional …

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 … WebOct 16, 2016 · We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in $\mathbb {R}^ {3}$: \ [ \partial_ {tt}u-\Delta...

WebarXiv:math/0404011v2 [math.AP] 23 Dec 2004 MAXIMIZERS FOR THE STRICHARTZ INEQUALITY DAMIANO FOSCHI Dipartimento di Matematica Pura e Applicata Universit`a di L’Aquila via Vetoio

WebFeb 1, 2024 · Let us consider the wave equation in R n × R: (1) { ∂ t 2 u − Δ u = 0, u ( x, 0) = f, ∂ t u ( x, 0) = g. The space–time estimate for the solution of (1) which is called Strichartz … gb18306—2001WebAug 8, 2024 · Abstract. We establish local-in-time Strichartz estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains with smooth … automatic transmission 2001 mustangWebWe 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 ... gb18380.12-2008WebStrichartz Estimates for Wave Equations with Charge Transfer Hamiltonians About this Title. Gong Chen. Publication: Memoirs of the American Mathematical Society ... As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial ... gb18383WebStrichartz estimates are spacetime estimates on homogeneous and inhomogeneous linear dispersive and wave equations. They are particularly useful for solving semilinear … automatic transmission gasket kit suppliersWebIn the present work, we establish the Strichartz estimates (2) for a range of subcritical p;q. The key tool is a microlocal parametrix construction previously used for the wave equation in [20] and [3]. This approach treats both Dirichlet and Neumann boundary conditions, and applies to general non-trapping obstacles. Theorem 1.1. Let automatic transmission 2005 nissan altimaWebSep 1, 2009 · Strichartz estimates are a family of space time integra- lity estimates on solutions u (t, x) : (âˆ’T ,T )Ã—Mâ†’C to the wave equation âˆ‚2t u (t, x)âˆ’ gu (t, x)= 0, u (0, x)= f (x), âˆ‚tu (0, x)= g (x), (1.1) here g denotes the Laplaceâ€“Beltrami operator on (M,g). gb18380