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Endpoint Strichartz estimates. (English) Zbl 0922.35028
Authors’ abstract: We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension \(n\geq 4)\) and the Schrödinger equation (in dimension \(n\geq 3\)). Three other applications are discussed: local existence for a nonlinear wave equation; and Strichartz-type estimates for more general dispersive equations and for the kinetic transport equation.

MSC:
35B45 A priori estimates in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
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