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

作者：Ribaud Francis^*; Vento Stephane

来源：Comptes Rendus Mathematique, 2012, 350(9-10): 499-503.

DOI：10.1016/j.crma.2012.05.007

In this Note we study the generalized 2D Zakharov-Kuznetsov equations partial derivative(t)u + Delta partial derivative(x)u + u(k)partial derivative(x)u = 0 for k %26gt;= 2. By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces H-s(R-2) for s %26gt; 1/4 if k = 2, s %26gt; 5/12 if k = 3 and s%26gt; 1 - 2/k if k %26gt;= 4.

• 出版日期2012-5