Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev Spaces

Mikael Signahl

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arXiv · 1409.3706

Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev Spaces

Mikael Signahl

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Abstract

In this paper we obtain global well-posedness in low order Sobolev spaces of higher order KdV type equations with dissipation. The result is optimal in the sense that the flow-map is not twice continuously differentiable in rougher spaces. The solution is shown to be smooth for positive times.

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Mikael Signahl. 2014-09-12. Almost Sharp Global Well-Posedness for a class of Dissipative and Dispersive Equations on R in Low Regularity Sobolev Spaces. https://arxiv.org/abs/1409.3706

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