ANISOTROPIC GEVREY REGULARITY FOR MKDV ON THE CIRCLE

作者：Hannah Heather^*; Himonas A Alexandrou; Petronilho Gerson

来源：Discrete and Continuous Dynamical Systems, 2011, 31: 634-642.

• Modified KdV equation
• mKdV
• Cauchy problem
• periodic
• Gevrey regularity
• Sobolev spaces

It is shown that the solution to the Cauchy problem for the modified Korteweg de Vries equation with initial data in an analytic Gevrey space G(sigma), sigma >= 1, as a function of the spacial variable belongs to the same Gevrey space. However, considered as function of time the solution does not belong to G(sigma). In fact, it belong to G(3 sigma) and not to any Gevrey space G(r), 1 <= r < 3 sigma.

• 出版日期2011-9