Analyticity and Smoothing Effect for the Coupled System of Equations of Korteweg-de Vries Type with a Single Point Singularity

作者：Alves Margareth S; Calsavara Bianca M R; Munoz Rivera Jaime E; Sepulveda Mauricio^*; Vera Villagran Octavio

来源：Acta Applicandae Mathematicae, 2011, 113(1): 75-100.

DOI：10.1007/s10440-010-9586-2

• Evolution equations
• Bourgain space
• Smoothing effect

Using Bourgain spaces and the generator of dilation P=3t a, (t) +x a, (x) , which almost commutes with the linear Korteweg-de Vries operator, we show that a solution of the initial value problem associated for the coupled system of equations of Korteweg-de Vries type which appears as a model to describe the strong interaction of weakly nonlinear long waves, has an analyticity in time and a smoothing effect up to real analyticity if the initial data only have a single point singularity at x=0.

• 出版日期2011-1