Well-posedness of the Fornberg-Whitham equation on the circle

作者：Holmes John M^*

来源：Journal of Differential Equations, 2016, 260(12): 8530-8549.

DOI：10.1016/j.jde.2016.02.030

• Well-posedness
• Initial value problem
• Sobolev spaces
• Multilinear estimates
• Kato-Ponce commutator
• Fomberg-Whitham equation

In this paper, we show that the Fornberg-Whithara equation is Well-posed in Sobolev spaces Hs, for s > 3/2, and in the periodic case. We then show that the Well-posedness is sharp in the sense that the continuity of the data-to-solution map is not better than continuous by using the method of approximate solutions. However, we also show that the solution map is Holder continuous in a weaker topology. These results are based on the Well-posedness result, as well as the solution size and lifespan estimates.

• 出版日期2016-6-15