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
| 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 defined definition dimensional eigenvalues estimate exists a constant exponential decay finite follows fractal dimension function grad H²(GR half balls Hausdorff Hausdorff dimension implies inequality inertial manifolds initial data Integrating interval j+k+e=0 Lebesgue measure Lemma Let us assume Let us consider Let us denote lim sup linear llull Lyapunov exponents Moreover Navier-Stokes equations obtain open set orthonormal Proof Proposition prove real number s₁ satisfies scalar product scale invariant sequence Sobolev spaces space Stokes equations Stokes formula Stokes operator Stokes system strong solution t,up Theorem to(luol u(to u₁ u₂ um(t uniqueness universal attractor vector volume elements weak solution δη δην λι νλι υλι Ω Ω