Abstract
In this paper we consider the Holm-Staley b-family of equations in the Sobolev spaces Hs (ℝ) for s >3/2. Using a geometric approach we show that, for any value of the parameter b, the corresponding solution map,u(0) ↦ u(T), is nowhere locally uniformly continuous.
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Inci, H. On the well-posedness of the Holm-Staley b-family of equations. J Nonlinear Math Phys 23, 213–233 (2016). https://doi.org/10.1080/14029251.2016.1161261
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DOI: https://doi.org/10.1080/14029251.2016.1161261