An initial boundary-value problem for the Zakharov-Kuznetsov equation

By Jean-Claude Saut, Roger Temam. Advances in Differential Equations, 2010

49 citations recorded by the source corpus.

We introduce and study an initial and boundary-value prob- lem for the Zakharov-Kuznetsov equation posed on an innite strip of R d+1 , d = 1; 2. After establishing a suitable trace theorem, we rst consider the linearized case and dene the corresponding semigroup on L 2 and prove that it has a global smoothing eect. Then we proceed to the nonlinear case and use the smoothing eect to prove in both di- mensions the existence of (unique when d = 1) global weak solutions of the initial and boundary problem with null boundary conditions and L 2 initial data.

Subfields: Electrical and Electronic Engineering, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8f8bf8008c22a34cd2a59a2642706ae8b3842d76

How researchers see this paper

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

In Mathematical Physics

1. Axel Grunrock
2. Sebastian Herr
3. S. Kinoshita
4. Didier Pilod
5. Carlos E. Kenig
6. Jonathan Bennett

In Statistical and Nonlinear Physics

1. Axel Grunrock
2. Sebastian Herr

Citations in the corpus

• 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.”