Title | Fundamental Directions in Mathematical Fluid Mechanics [electronic resource] / edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8424-2 |
Descript | VIII, 293 p. online resource |
An Introduction to the Navier-Stokes Initial-Boundary Value Problem -- 0 Introduction -- 1 Some considerations on the structure of the Navier-Stokes equations -- 2 The Leray-Hopf weak solutions and related properties -- 3 Existence of weak solutions -- 4 The energy equality and uniqueness of weak solutions -- 5 Regularity of weak solutions -- 6 More regular solutions and the โthรฉorรจme de structureโ -- 7 Existence in the class Lr (0,T; Ls(?), 2/r +n/s = 1, and further regularity properties -- References -- Spectral Approximation of Navier-Stokes Equations -- 1 Mathematical foundation and different paradigms of spectral methods -- 2 Stokes and Navier-Stokes equations -- 3 Time-differentiation of Navier Stokes equations -- 4 Domain decomposition methods -- 5 Numerical results -- References -- Simple Proofs of Bifurcation Theorems -- 1 Introduction -- 2 Bifurcation of equilibrium solutions -- 3 Bifurcation of periodic solutions -- 4 Generalizations -- Appendix A: Proof of Proposition 3.1 -- References -- On The Steady Transport Equation -- 1 Introduction -- 2 Existence in W1,2 ? Lq for the scalar transport equation -- 3 Existence in W1,2 ? Lq for the scalar transport equation -- 4 Estimates for ???2,2, ???? and ?????1,2 -- 5 Existence in Wm,2 (?), for any fixed m -- 6 Integration along characteristics -- References -- On the Existence and Uniqueness Theory for the Steady Compressible Viscous Flow -- 1 Introduction -- 2 Poisson-Stokes equations for isothermal flow -- 3 Main result -- 4 Iterative scheme -- 5 Regularity lemmas -- 6 Bounds for the iterates -- 7 Convergence of the iterates -- 8 Uniqueness in the ball of existence -- 9 Uniqueness reconsidered directly -- References -- Finite Element Methods for the Incompressible Navier-Stokes Equations -- 1 Introduction -- 2 Models of viscous flow -- 3 Spatial discretization by finite elements -- 4 Time discretization and linearization -- 5 Solution of the algebraic systems -- 6 A review of theoretical analysis -- 7 Error control and mesh adaptation -- 8 Extension to weakly compressible flows -- References