ON INNER REGULARITY OF SOLUTIONS OF TWO-DIMENSIONAL ZAKHAROV -- KUZNETSOV EQUATION

In this paper, we consider questions of inner regularity of weak solutions of initial-boundary value problems for the Zakharov -- Kuznetsov equation with two spatial variables. The initial function is assumed to be irregular, and the main parameter governing the regularity is the decay rate of the initial function at infinity. The main results of the paper are obtained for the problem on a half-strip. In this problem, different types of initial conditions (e.g., Dirichlet or Neumann conditions) influence the inner regularity. We also give a survey of earlier results for other types of domains: a plane, a half-plane, and a strip.
CONTENTS 1. Introduction 313 2. Half-Strip Initial-Boundary Value Problems 317 3. Half-Plane Initial-Boundary Value Problems 335 4. Cauchy Problem 339 5. Strip Initial-Boundary Value Problems 341 References 342 1. Introduction [...]