The three-dimensional Navier-Stokes equations : classical theory
著者
書誌事項
The three-dimensional Navier-Stokes equations : classical theory
(Cambridge studies in advanced mathematics, 157)
Cambridge University Press, 2016
- : hardback
大学図書館所蔵 全32件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 457-466) and index
内容説明・目次
内容説明
A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier-Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray-Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.
目次
- Part I. Weak and Strong Solutions: 1. Function spaces
- 2. The Helmholtz-Weyl decomposition
- 3. Weak formulation
- 4. Existence of weak solutions
- 5. The pressure
- 6. Existence of strong solutions
- 7. Regularity of strong solutions
- 8. Epochs of regularity and Serrin's condition
- 9. Robustness of regularity
- 10. Local existence and uniqueness in H1/2
- 11. Local existence and uniqueness in L3
- Part II. Local and Partial Regularity: 12. Vorticity
- 13. The Serrin condition for local regularity
- 14. The local energy inequality
- 15. Partial regularity I - dimB(S) 5/3
- 16. Partial regularity II - dimH(S) 1
- 17. Lagrangian trajectories
- A. Functional analysis: miscellaneous results
- B. Calderon-Zygmund Theory
- C. Elliptic equations
- D. Estimates for the heat equation
- E. A measurable-selection theorem
- Solutions to exercises
- References
- Index.
「Nielsen BookData」 より