The Cauchy problem for the 3D Zakharov-Kuznetsov equation

By Felipe Linares, Jean-Claude Saut. 2009

117 citations recorded by the source corpus.

We prove that the Cauchy problem for the three-dimensional Zakharov-Kuznetsov equation is locally well-posed for data in $H^s(\R^3)$, s > $\frac{9}{8}$.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/eb80d843575a4807a2162d65b62f879aafbf91c5

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Well-Posedness for the ZK Equation in a Cylinder and on the Background of a KdV Soliton (2010, methodology): “From this point on, one can use similar arguments as in Kenig [7] or Linares and Saut [11] for proving the following result.”
The Fourier restriction norm method for the Zakharov-Kuznetsov equation (2013, methodology): “The three-dimensional version of the Cauchy problem (1) was shown to be locally well-posed in H(R(3)) for s > 9 8 by Linares and Saut in [18], where they used the”
Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D (2019, background): “In the three dimensional case (n = 3), Linares and Saut [20] showed the local well-posedness in H(R) for s > 9/8.”
The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation (2012, background): “2 See [7, 21, 24] for the Cauchy theory in larger spaces.”