KPZ equation with fractional derivatives of white noise (Mathematical Analysis of Viscous Incompressible Fluid)

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説明

In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order $gamma$>0 in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer [3] as an application of the theory of regularity structures. Our aim is to see to what extent his theory works if noises become rougher. We can expect that his theory works if and only if $gamma$<1/2. However, we show that the renormalization like (partial_{x}h)^{2}-infty is well-posed only if $gamma$<1/4.

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詳細情報 詳細情報について

  • CRID
    1050564285811068544
  • NII論文ID
    120006477741
  • NII書誌ID
    AN00061013
  • ISSN
    18802818
  • HANDLE
    2433/231567
  • 本文言語コード
    en
  • 資料種別
    departmental bulletin paper
  • データソース種別
    • IRDB
    • CiNii Articles

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