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Displaying similar documents to “Comparison of KP and BBM-KP models.”

Bilinear estimates related to the KP equations

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.

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 H ^ s r ℝ defined by the norm v 0 H ^ s r ℝ : = ξ s v 0 ^ L ξ r ' , ξ = 1 + ξ 2 1 2 , 1 r + 1 r ' = 1 . Local well-posedness for the jth equation is shown in the parameter range 2 ≥ 1, r > 1, s ≥ 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 < 2 j - 1 2 r ' . The results for r =...