Bilinear estimates in dyadic BMO and the Navier-Stokes equations

• Nakai Eiichi

  Department of Mathematics, Osaka Kyoiku University

• Yoneda Tsuyoshi

  Department of Mathematics and Statistics, University of Victoria

抄録

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.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

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

  一般社団法人 日本数学会

キーワード

• Navier-Stokes equation
• bounded mean oscillation
• dyadic BMO
• bilinear estimate

詳細情報

• CRID: 1390001205116423552
• NII論文ID: 10030740240
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06420399
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 023596717
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I023596717
• 本文言語コード: en
• データソース種別:
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