Bilinear estimates related to the KP equations

Nikolay Tzvetkov

Displaying similar documents to “Bilinear estimates related to the KP equations”

On the local well-posedness of the KP equations

Nikolay Tzvetkov (2000-2001)

Séminaire Équations aux dérivées partielles

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Unique local existence of solution in low regularity space of the Cauchy problem for the mKdV equation with periodic boundary condition

Kenji Nakanishi, Hideo Takaoka, Yoshio Tsutsumi (2007-2008)

Séminaire Équations aux dérivées partielles

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On the hierarchies of higher order mKdV and KdV equations

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 ${\hat{H}}_{s}^{r} (ℝ)$ defined by the norm ${∥v_{0}∥}_{{\hat{H}}_{s}^{r} (ℝ)} : = {∥{〈ξ〉}^{s} \hat{v_{0}}∥}_{L_{ξ}^{r^{'}}}, 〈ξ〉 = {(1 + ξ^{2})}^{\frac{1}{2}}, \frac{1}{r} + \frac{1}{r^{'}} = 1$ . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ $\frac{2 j - 1}{2 r^{'}}$ . 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 < $\frac{2 j - 1}{2 r^{'}}$ . The results for r =...

Comparison of KP and BBM-KP models.

Daspan, Gideon P., Tom, Michael M. (2007)

International Journal of Mathematics and Mathematical Sciences

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Remarks on the Klein-Gordon equation

Lars Hörmander (1987)

Journées équations aux dérivées partielles

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Local existence theory for the generalized Schrödinger equation

Gustavo Ponce (1997)

Journées équations aux dérivées partielles

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On KP-II type equations on cylinders

Axel Grünrock, Mahendra Panthee, Jorge Drumond Silva (2009)

Annales de l'I.H.P. Analyse non linéaire

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