A Note on the Cauchy problem for the 2D generalized Zakharov–Kuznetsov equations

By Stéphane Vento, Francis Ribaud. 2011

79 citations recorded by the source corpus.

Abstract In this Note we study the generalized 2D Zakharov–Kuznetsov equations ∂ t u + Δ ∂ x u + u k ∂ x u = 0 for k ⩾ 2 . By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces H s ( R 2 ) for s > 1 / 4 if k = 2 , s > 5 / 12 if k = 3 and s > 1 − 2 / k if k ⩾ 4 .

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

View Paper: https://www.semanticscholar.org/paper/67b9013207d4f9e3826faf9d27cdd24d44c914b7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D (2019, methodology): “After that, Ribaud and Vento [23] improved the necessary regularity condition by showing the local well-posedness in H(R) for s > 1/4.”
The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation (2012, methodology): “We also refer to [22] for solutions on a nontrivial background and to [20] and [25] for well-posedness results of the Cauchy problem for generalized Zakharov-Kuznetsov equations in R(2).”
The Fourier restriction norm method for the Zakharov-Kuznetsov equation (2013, background): “Without attempting to be complete we refer to the papers [23, 4, 2, 19, 5, 15, 17, 22, 16, 21] and references therein.”