Applied Analysis of the Navier-Stokes EquationsCambridge University Press, 1995 - 217 ページ The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the fundamental dynamics of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier-Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. The goal of the book is to present a mathematically rigorous investigation of the Navier-Stokes equations that is accessible to a broader audience than just the subfields of mathematics to which it has traditionally been restricted. Therefore, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses. This book is appropriate for graduate students in many areas of mathematics, physics, and engineering. |
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1 | 5 |
4 | 14 |
1 | 19 |
2223 | 26 |
3 | 38 |
3 | 45 |
1 | 61 |
3 | 96 |
3 | 124 |
6 | 132 |
2 | 138 |
3 | 144 |
8 | 156 |
4 | 165 |
3 | 177 |
Appendix A Inequalities | 205 |
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amplitude analysis attractor dimension average body force Boussinesq equations calculus inequalities Chapter component Couette flow curl d²x dªx defined density derivatives differential inequality dimensionless divergence-free dynamical system eigenvalue energy dissipation rate enstrophy estimate Euler equations evolution equation exponentially F₁ finite fixed points flow field fluid Foias function Galerkin approximations global attractor gradient high Reynolds number high wavenumber incompressible infinitesimal initial condition kinetic energy Kolmogorov length L2 norm ladder Laplacian Lemma length scale linear stability Lipschitz condition Lorenz equations Lyapunov exponents Navier-Stokes equations no-slip nonlinear stability nonlinear terms number of degrees parameter periodic boundary conditions perturbation Picard iterates problem quantity Rayleigh number Reynolds stress satisfies square integrable Temam temperature theorem theory unique upper bound vanishes variables vector field velocity field velocity scale velocity vector field viscosity vortex stretching vorticity wavenumber weak solutions ди