Displaying similar documents to “Uniform estimates for a class of evolution equations”

The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation

Daniel Tataru (1999)

Journées équations aux dérivées partielles

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The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness...

Self-similar solutions and Besov spaces for semi-linear Schrödinger and wave equations

Fabrice Planchon (1999)

Journées équations aux dérivées partielles

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We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space B ˙ 2 n 2 - 2 p , ( 𝐑 n ) , when the nonlinearity is of type u p , for p 𝐍 . This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.