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A rigidity result for the Holm-Staley b-family of equations with application to the asymptotic stability of the Degasperis-Procesi peakon

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 نشر من قبل Luc Molinet
 تاريخ النشر 2018
  مجال البحث
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 تأليف Luc Molinet




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We prove that the peakons are asymptotically H 1-stable, under the flow of the Degasperis-Procesi equation, in the class of functions with a momentum density that belongs to M + (R). The key argument is a rigidity result for uniformly in time exponentially decaying global solutions that is shared by the Holm-Staley b-family of equations for b $ge$ 1. This extends previous results obtained for the Camassa-Holm equation (b = 2).



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