Navier-Stokes EquationsBoth an original contribution and a lucid introduction to mathematical aspects of fluid mechanics, Navier-Stokes Equations provides a compact and self-contained course on these classical, nonlinear, partial differential equations, which are used to describe and analyze fluid dynamics and the flow of gases. |
Contents
CHAPTER 1 Notation and Preliminary Material | 1 |
CHAPTER 2 The Stokes equations Existence and Uniqueness of Weak Solutions | 11 |
CHAPTER 3 Regularity of Solutions of the Stokes Equations | 14 |
CHAPTER 4 The Stokes Operator | 31 |
CHAPTER 5 The NavierStokes Equations | 45 |
CHAPTER 6 Inequalities for the Nonlinear Term | 48 |
CHAPTER 7 Stationary solutions to the NavierStokes Equations | 57 |
CHAPTER 8 Weak Solutions of the NavierStokes Equations | 63 |
CHAPTER 10 Further Results Concerning Weak and Strong Solutions | 83 |
CHAPTER 11 Vanishing Viscosity Limits | 99 |
CHAPTER 12 Analyticity and Backward Uniqueness | 104 |
CHAPTER 13 Exponential Decay of Volume Elements | 110 |
CHAPTER 14 Global Lyapunov Exponents Hausdorff and Fractal Dimension of the Universal Attractor | 133 |
CHAPTER 15 Inertial Manifolds | 154 |
Bibliography | 185 |
| 189 | |
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Common terms and phrases
Am+1 arbitrary bounded set class C² Clearly Cm,x compact compute converges defined dimensional eigenvalues estimate exists a constant exponential decay finite follows fractal dimension function grad H²(GR half balls Hausdorff Hausdorff dimension HN+1 implies inequality inertial manifolds initial data Integrating interval L²(GR Lebesgue measure Lemma Let us assume Let us consider Let us denote lim sup linear llull Lyapunov exponents Navier-Stokes equations obtain open bounded open set orthogonal orthonormal projector Proof Proposition prove s₁ satisfies scalar product scale invariant sequence space Stokes equations Stokes formula Stokes operator Stokes system strong solution t,up Theorem u(to u₁ u₂ um(t uniqueness universal attractor vector volume elements weak solution weakly δη ν ν νλι υλι