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- Équipes
- Productions scientifiques
- Événements
- Séminaires

members:lemarie:ns21toc

- Regularity of the three-dimensional fluid flows: a mathematical challenge for the 21st century
- The Clay Millennium Prizes
- The Clay Millennium Prize for the Navier–Stokes equations
- Boundaries and the Navier–Stokes Clay Millennium Problem

- Frames of references
- The convection theorem
- Conservation of mass
- Newton's second law
- Pressure
- Strain
- Stress
- The equations of hydrodynamics
- The Navier–Stokes equations
- Vorticity
- Boundary terms
- Blow up
- Turbulence

- Mechanics in the Scientific Revolution era
- Bernoulli's Hydrodymica
- D'Alembert
- Euler
- Laplacian physics
- Navier, Cauchy, Poisson, Saint-Venant, and Stokes
- Reynolds
- Oseen, Leray, Hopf, and Ladyzhenskaya
- Turbulence models

- The heat kernel
- The Poisson equation
- The Helmholtz decomposition
- The Stokes equation
- The Oseen tensor
- Classical solutions for the Navier–Stokes problem
- Small data and global solutions
- Time asymptotics for global solutions
- Steady solutions
- Spatial asymptotics
- Spatial asymptotics for the vorticity
- Intermediate conclusion

- The integral Navier–Stokes problem
- Quadratic equations in Banach spaces
- A capacitary approach of quadratic integral equations
- Generalized Riesz potentials on spaces of homogeneous type
- Dominating functions for the Navier–Stokes integral equations
- A proof of Oseen's theorem through dominating functions
- Functional spaces and multipliers

- Uniform local estimates
- Heat equation
- Stokes equations
- Oseen equations
- Very weak solutions for the Navier–Stokes equations
- Mild solutions for the Navier–Stokes equations
- Suitable solutions for the Navier–Stokes equations

- Kato's mild solutions
- Local solutions in the Hilbertian setting
- Global solutions in the Hilbertian setting
- Sobolev spaces
- A commutator estimate
- Lebesgue spaces
- Maximal functions
- Basic lemmas on real interpolation spaces
- Uniqueness of L^3 solutions

- Morrey spaces
- Morrey spaces and maximal functions
- Uniqueness of Morrey solutions
- Besov spaces
- Regular Besov spaces
- Triebel–Lizorkin spaces
- Fourier transform and Navier–Stokes equations

- Koch and Tataru's theorem
- Q-spaces
- A special subclass of BMO^-1
- Ill-posedness
- Further results on ill-posedness
- Large data for mild solutions
- Stability of global solutions
- Analyticity
- Small data

- Symmetries for the Navier–Stokes equations
- Two-and-a-half dimensional flows
- Axisymmetrical solutions
- Helical solutions
- Brandolese's symmetrical solutions
- Self-similar solutions
- Stationary solutions
- Landau's solutions of the Navier–Stokes equations
- Time-periodic solutions
- Beltrami flows

- First criteria
- Blow up for the cheap Navier–Stokes equation
- Serrin's criterion
- Some further generalizations of Serrin's criterion
- Vorticity
- Squirts

- The Rellich lemma
- Leray's weak solutions
- Weak-strong uniqueness: the Prodi–Serrin criterion
- Weak-strong uniqueness and Morrey spaces on the product space R × R^3
- Almost strong solutions
- Weak perturbations of mild solutions

- Interior regularity
- Serrin's theorem on interior regularity
- O'Leary's theorem on interior regularity
- Further results on parabolic Morrey spaces
- Hausdorff measures
- Singular times
- The local energy inequality
- The Caffarelli–Kohn–Nirenberg theorem on partial regularity
- Proof of the Caffarelli–Kohn–Nirenberg criterion
- Parabolic Hausdorff dimension of the set of singular points
- On the role of the pressure in the Caffarelli, Kohn, and Nirenberg regularity theorem

- Uniformly locally square integrable solutions
- Local inequalities for local Leray solutions
- The Caffarelli, Kohn, and Nirenberg ε-regularity criterion
- A weak-strong uniqueness result

- Local Leray solutions with an initial value in L^3
- Critical elements for the blow up of the Cauchy problem in L^3
- Backward uniqueness for local Leray solutions
- Seregin's theorem
- Known results on the Cauchy problem for the Navier–Stokes equations in presence of a force
- Local estimates for suitable solutions
- Uniqueness for suitable solutions
- A quantitative one-scale estimate for the Caffarelli–Kohn–Nirenberg regularity criterion
- The topological structure of the set of suitable solutions
- Escauriaza, Seregin, and Šverák's theorem

- The Leray–Schauder principle
- Steady-state solutions
- Self-similarity
- Statement of Jia and Šverák's theorem
- The case of locally bounded initial data
- The case of rough data
- Non-existence of backward self-similar solutions

- Global existence, uniqueness and convergence issues for approximated equations
- Leray's mollification and the Leray-α model
- The Navier–Stokes α -model
- The Clark- α model
- The simplified Bardina model
- Reynolds tensor

- Faedo–Galerkin approximations
- Frequency cut-off
- Hyperviscosity
- Ladyzhenskaya's model
- Damped Navier–Stokes equations

- Temam's model
- Vishik and Fursikov's model
- Hyperbolic approximation

- Energy inequalities
- Critical spaces for mild solutions
- Models for the (potential) blow up
- The method of critical elements

members/lemarie/ns21toc.txt · Last modified: 2016/03/23 19:30 by Pierre Gilles Lemarié

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