Initial-Boundary Value Problems and the Navier-Stokes EquationThis book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis. |
Contents
CL47_ch1 | 1 |
CL47_ch2 | 23 |
CL47_ch3 | 81 |
CL47_ch4 | 121 |
CL47_ch5 | 159 |
CL47_ch6 | 177 |
CL47_ch7 | 203 |
CL47_ch8 | 275 |
CL47_ch9 | 325 |
CL47_ch10 | 345 |
CL47_appendix1 | 361 |
CL47_appendix2 | 365 |
CL47_appendix3 | 371 |
CL47_appendix4 | 389 |
CL47_backmatter | 393 |
Other editions - View all
Initial-boundary Value Problems and the Navier-Stokes Equations Heinz-Otto Kreiss,Jens Lorenz Limited preview - 1989 |
Initial-boundary Value Problems and the Navier-Stokes Equations, Volume 136 Heinz-Otto Kreiss,Jens Lorenz No preview available - 1989 |
Common terms and phrases
1-periodic apply assume assumption B₁ basic energy estimate boundary conditions bounded C-smooth c₁ Cauchy problem characteristic coefficients consider const constant constant-coefficient convergence defined denote depend Duhamel's principle eigenvalues example existence finite follows Fourier grad gridfunctions half-space half-space problem Hermitian matrix hyperbolic systems incompressible independent inhomogeneous initial condition initial data initial-boundary value problem integration interval inviscid K₁ Kreiss L2-norm Laplace transform lower-order terms Math matrix maximum norm N-S equations Navier-Stokes equations nonlinear nonsingular norm notation obtain operator P(iw parabolic systems Parseval's relation partial differential equations periodic Cauchy problem priori estimates problem is well-posed Proof prove result satisfies scalar Section sequence smooth function Sobolev inequality solves space dimensions strip problem strongly hyperbolic strongly well-posed Suppose Theorem u₁ unique solution v₁ variable-coefficient variables vector weak solution well-posed problems well-posedness