Cubic Quasilinear wave equation and bilinear estimates
Hajer Bahouri, Jean-Yves Chemin (2000-2001)
Séminaire Équations aux dérivées partielles
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Hajer Bahouri, Jean-Yves Chemin (2000-2001)
Séminaire 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 =...
Jerry L. Bona, Zoran Grujić, Henrik Kalisch (2005)
Annales de l'I.H.P. Analyse non linéaire
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Jakubassa-Amundsen, D.H. (2005)
Documenta Mathematica
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Othmar Koch, Christian Lubich (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional nuclear wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of low-dimensional nonlinear partial...
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...