相關主題
商品描述
The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR, described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However, theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.
商品描述(中文翻譯)
本專著的主要目標是發展一種基本且自足的方法，來探討在歐幾里得空間 R 中的粘性不可壓縮流體的數學理論，該理論由 Navier-Stokes 方程描述。本書主要針對熟悉希爾伯特空間和巴拿赫空間中基本泛函分析工具的學生。然而，為了方便讀者，在前兩章中我們收集了一些 Sobolev 空間、分佈、算子等的基本性質，並不提供證明。另一個重要目標是為完全一般的區域 ? 來制定理論。特別地，該理論適用於任意無界的非光滑區域。因此，在非線性情況下，我們必須將自己限制在物理上最重要的空間維度 n=2,3。為了數學上的一般性，我們將為所有 n ≥ 2 發展線性化理論。儘管這裡發展的泛函分析方法原則上對專家來說是已知的，但其系統性的處理並不可得，甚至可用的各種方面也散佈在文獻中。然而，文獻非常廣泛，我甚至沒有嘗試列出所有相關的論文，因為這可能會讓學生感到困惑。在這方面，我想對未能引用所有直接或間接啟發本專著的作品表示歉意。
作者簡介
Hermann Sohr is professor of mathematics, especially mathematical fluid mechanics, at the University Paderborn, Germany.
作者簡介(中文翻譯)
赫爾曼·索爾（Hermann Sohr）是德國帕德博恩大學（University Paderborn）數學教授，專門研究數學流體力學。
