Non linear evolution equations Cauchy problem and scattering theory
J. Ginibre, G. Velo (1983-1984)
Séminaire Équations aux dérivées partielles (Polytechnique)
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J. Ginibre, G. Velo (1983-1984)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Nikolay Tzvetkov (2000)
Journées équations aux dérivées partielles
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We survey some recent results for the KP-II equation. We also give an idea for treating the “bad frequency interactions” of the bilinear estimates in the Fourier transform restriction spaces related to the KP-I 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...
Kenji Nakanishi, Hideo Takaoka, Yoshio Tsutsumi (2007-2008)
Séminaire Équations aux dérivées partielles
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Christopher D. Sogge (1993)
Journées équations aux dérivées partielles
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Axel Grünrock (2010)
Open Mathematics
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The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces defined by the norm . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ . The proof uses an appropriate variant of the Fourier restriction norm method. A counterexample is discussed to show that the Cauchy problem for equations of this type is in general ill-posed in the C 0-uniform sense, if s < . The results for r =...
P. Brenner (1988-1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
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