Bilinear estimates in dyadic BMO and the Navier-Stokes equations

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Author(s)

Abstract

We establish bilinear estimates in dyadic BMO as an extension of Kozono and Taniuchi’s result on the usual BMO. To establish the bilinear estimates we use sharp maximal functions, while they used the boundedness of pseudo-differential operators by Coifman and Meyer. By this extension we prove that the dyadic BMO norm of the velocity controls the blow-up phenomena of smooth solutions to the Navier-Stokes equations. Moreover, we give an odd function with type II singularity which clarifies the difference between BMO and dyadic BMO.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 64(2), 399-422, 2012-04-01

    The Mathematical Society of Japan

References:  15

Codes

  • NII Article ID (NAID)
    10030740240
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    023596717
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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