The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation
Tataru, Daniel
Journées équations aux dérivées partielles, (1999), p. 1-16 / Harvested from Numdam
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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 for initial data which is less regular than the classical threshold.

Publié le : 1999-01-01
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     author = {Tataru, Daniel},
     title = {The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1999},
     pages = {1-16},
     mrnumber = {2000h:35114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_1999____A14_0}
}

Tataru, Daniel. The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation. Journées équations aux dérivées partielles,  (1999), pp. 1-16. http://gdmltest.u-ga.fr/item/JEDP_1999____A14_0/

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