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Lecture notes on regularity theory for the Navier-Stokes equations /
The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes eq...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
[2014]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 Helmholtz-Weyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. Non-Linear Stationary Problem; 3.1 Existence of Weak Solutions.
- 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear Non-Stationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Non-linear Non-Stationary Problem; 5.1 Compactness Results for Non-Stationary Problems; 5.2 Auxiliary Problem; 5.3 Weak Leray-Hopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak Leray-Hopf Solutions. 2D Case; 5.6 Further Properties of Weak Leray-Hopf Solutions.
- Appendix A Backward Uniqueness and Unique ContinuationA. 1 Carleman-Type Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B Lemarie-Riesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index.