L[q]-L[r] estimate of the Oseen flow in plane exterior domains

• Hishida Toshiaki

  Graduate School of Mathematics, Nagoya University

書誌事項

タイトル別名

• <i>L</i>^<i>q</i>-<i>L</i>^<i>r</i> estimate of the Oseen flow in plane exterior domains

抄録

We consider the initial value problem for the Oseen system in plane exterior domains and study the large time behavior of solutions. For the space dimension n ≥ 3 the theory was well developed by [26], [10] and [11], while 2D case has remained open because of difficulty arising from singularity like log √(λ+α²) of the Oseen resolvent, where λ is the resolvent parameter and α is the Oseen parameter. In this paper we derive the local energy decay of the Oseen semigroup and apply it to deduction of L^q-L^r estimates. The dependence of estimates on the Oseen parameter α is also discussed. The proof relies on detailed analysis of asymptotic structure of the fundamental solution of the Oseen resolvent with respect to both λ and α.

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 68 (1), 295-346, 2016

  一般社団法人 日本数学会

キーワード

• Oseen semigroup
• plane exterior domain
• decay

詳細情報

• CRID: 1390282680092484096
• NII論文ID: 130005122692
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/06810295
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL書誌ID: 027060786
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I027060786
• 本文言語コード: en
• データソース種別:
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