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  • THE INVISCID LIMIT OF THE MODIFIED BENJAMIN–ONO–BURGERS EQUATION

  • Part of
  • HUA ZHANG, YUQIN KE
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 83 / Issue 2 / April 2011
    Published online by Cambridge University Press:
    06 December 2010, pp. 301-320
    Print publication:
    April 2011
    • Article
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  • We prove that the modified Benjamin–Ono–Burgers equation is globally well-posed in Hs for s>0. Moreover, we show that the solution of the modified Benjamin–Ono–Burgers equation converges to that of the modified Benjamin–Ono equation in the natural space C([0,T];Hs), s≥1/2, as the dissipative coefficient ϵ goes to zero, provided that the L2 norm of the initial data is sufficiently small.