Alphabeta MathPeriodic smooth incompressible energy identity
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1 · Prerequisites
- Absolute and Conditional Convergence; Rearrangement; Products
- Approximation and Compactness in C(K)
- Areas of Elementary Plane Figures
- Binary Operations, Monoids, Groups and Subgroups
- Bounded Linear Operators and Quotient Spaces
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2 · Logical flowchart
3 · Items
Lemma
Mean-zero Poincare inequality on the normalized torus
Theorem
Periodic smooth incompressible energy identity
Theorem
Smooth incompressible and symmetric-system stability
Theorem
Smooth Sobolev continuation criterion
Theorem
Controlled periodic smooth inviscid limit
Theorem
Smooth vorticity identities and two-dimensional norms
Theorem
Smooth polytropic energy conservation
Theorem
Conditional wall energy and smooth uniqueness
Proposition
Fluid equation scalings and dimensionless numbers
Lemma
Two-dimensional Fourier logarithmic velocity bound
Lemma
Two-dimensional transport commutator bound by the Fourier l1 gradient sum
Theorem
Global smooth two-dimensional periodic Navier–Stokes
Sources
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, §2.1.7
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, §2.1.5, Exercise 2.1.14
- Thomas Y. Hou, lecture notes, Blow-up or no blow-up?, energy identity (3.1)
- David Tong, Fluid Mechanics, Chapter 2, §3.1.2
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, §2.1.5
- Thomas Y. Hou, lecture notes, Blow-up or no blow-up?, §3
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, Chapter 2, §§2.1.5–2.1.6
- David Tong, Fluid Mechanics, Chapter 2
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, Chapter 2, §2.1.5
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, Chapter 2, §2.1.6
- Thomas Y. Hou, lecture notes, Blow-up or no blow-up?, equations (3.1)–(3.4)
- David Tong, Fluid Mechanics, Chapter 3, §4.5
- François Golse, The Boltzmann Equation and Its Hydrodynamic Limits, Chapter 3
- David Tong, Fluid Mechanics, Chapter 2, §§3.1.1–3.1.2
- David Tong, Fluid Mechanics, Chapter 2, §3.3.1
- David Tong, Fluid Mechanics, Chapter 3, §4.4.4
- Sergei Kuksin and Armen Shirikyan, Mathematics of Two-Dimensional Turbulence, Chapter 2, §2.1.6, Theorem 2.1.18
- Thomas Y. Hou, Blow-up or no blow-up?, lecture notes, §3