摘要: An Introduction to the Navier-Stokes Initial-Boundary Value Problem.- 0 Introduction.- 1 Some considerations on structure of equations.- 2 The Leray-Hopf weak solutions and related properties.- 3 Existence solutions.- 4 energy equality uniqueness 5 Regularity 6 More regular "theoreme de structure".- 7 in class Lr (0,T Ls(?), 2/r +n/s = 1, further regularity References.- Spectral Approximation Equations.- Mathematical foundation different paradigms spectral methods.- Stokes Time-differentiation Navier Domain decomposition Numerical results.- Simple Proofs Bifurcation Theorems.- equilibrium periodic Generalizations.- Appendix A: Proof Proposition 3.1.- On Steady Transport Equation.- W1,2 ? Lq for scalar transport equation.- Estimates ???2,2, ???? ?????1,2.- Wm,2 (?), any fixed m.- Integration along characteristics.- Uniqueness Theory Compressible Viscous Flow.- Poisson-Stokes equations isothermal flow.- Main result.- Iterative scheme.- lemmas.- Bounds iterates.- Convergence 8 ball existence.- 9 reconsidered directly.- Finite Element Methods Incompressible Models viscous Spatial discretization by finite elements.- Time linearization.- Solution algebraic systems.- A review theoretical analysis.- Error control mesh adaptation.- Extension weakly compressible flows.- References.
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