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Non-uniform continuity of the data-to-solution map for CH and the Euler equations

PDE and Applied Math Seminar

Speaker: Alex Himonas, Notre Dame
Location: 1147 MSB
Start time: Tue, Jan 5 2010, 4:10PM

Abstract. We shall discuss the Cauchy problems for the Camassa-Holm (CH) and the Euler equations. More precisely, we shall prove that the data-to-solution map for these equations is not uniformly continuous in Sobolev spaces for any exponent greater than the well-posedness index. Considering the fact that these equations are well-posed with continuous dependence on initial data, our results make this dependence optimal. This talk is based on recent work with Carlos Kenig and Gerard Misiolek.