Symmetry Problems. the Navier-Stokes Problem.
暫譯: 對稱性問題:納維-斯托克斯問題
Ramm, Alexander G., Krantz, Steven G.
- 出版商: Morgan & Claypool
- 出版日期: 2019-03-05
- 售價: $1,610
- 貴賓價: 9.5 折 $1,530
- 語言: 英文
- 頁數: 85
- 裝訂: Quality Paper - also called trade paper
- ISBN: 1681735059
- ISBN-13: 9781681735054
海外代購書籍(需單獨結帳)
商品描述
This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ3. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.
商品描述(中文翻譯)
本書提供了散射振幅的必要且充分條件,以判斷散射體是否為球對稱。這裡的散射體指的是一種潛能或障礙物。它還提供了在此區域內,若海姆霍茲方程的過確定邊界問題可解,則該區域為球體的必要且充分條件。這包括對施費爾猜想的證明、龐佩尤問題的解以及其他偏微分方程的對稱問題。接著,本書研究了一些與潛能理論相關的其他對稱問題。其中包括「隱形障礙物」的問題。在第五章中,提供了在 ℝ³ 中的納維-斯托克斯問題的解。作者證明了如果數據是光滑的且衰減得足夠快,則該問題具有唯一的全局解。書中還包含了納維-斯托克斯問題解的全新 a priori 估計。最後,該書提供了潛能理論的逆問題的解,無需對均質體的星形假設進行標準假設。