Everything about NavierāStokes existence and smoothness
Millennium Prize Problem
The question of whether the NavierāStokes equations always have smooth solutions in three-dimensional Euclidean space, given some initial conditions and possibly an external force, has been a longstanding unsolved problem in mathematics since the early 20th century. The equations are a system of partial differential equations that describe the motion of a fluid in space. Although computational solutions to the NavierāStokes equations are used in a large number of practical applications, there is no complete analytical understanding of the solutions. In particular, solutions of the NavierāStokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. Wikipedia ā
š§ Start here: a 6-step reading path
- Read the overview: NavierāStokes existence and smoothnessA 5-minute orientation
- Skim a recent paper: A canonical Hamiltonian formulation of the NavierāStokes problemInfluential work since 2022
- Pick up a classic book: Tetrahedral finite-volume solutions to the Navier-Stokes equations on complex configurationsThe most-reprinted book on the subject
- Read the landmark paper: Stabilized mixed methods for the Stokes problemCited 223 times
- Go sideways: Millennium Prize ProblemsA closely related topic
- Go sideways: NavierāStokes equationsA closely related topic
š Definitions
No dictionary entry for this exact phrase.
šļø The subject at a glance
š Landmark papers (most cited)
Stabilized mixed methods for the Stokes problem
An efficient smoother for the Stokes problem
The 3D Navier-Stokes Problem
On the stokes problem in Lipschitz domains
Analysis of a Stokes interface problem
Stokes problem for elastico-viscous fluid
Nonconforming finite elements for the Stokes problem
Stokes' first problem for viscoelastic fluids
š Influential since 2022
A canonical Hamiltonian formulation of the NavierāStokes problem
Shape Optimization of the Stokes Eigenvalue Problem
Meshless Galerkin analysis of the generalized Stokes problem
Hybridizable discontinuous Galerkin methods for the coupled StokesāBiot problem
Conforming virtual element approximations of the two-dimensional Stokes problem
š Books worth reading
- šTetrahedral finite-volume solutions to the Navier-Stokes equations on complex configurationsNeal T. Frink Ā· 1998
Matematicheskie voprosy dinamiki viļø aļø”zkoÄ neszhimaemoÄ zhidkostiO. A. LadyzhenskaiĶ”a Ā· 1961
Compressible Navier-Stokes EquationsPavel Plotnikov Ā· 2012
Diffusion and ecological problemsAkira OĢkubo, Akira Okubo Ā· 1980
Initial-boundary value problems and the Navier-Stokes equationsH. Kreiss Ā· 1989- šA multidomain spectral collocation method for the Stokes problemG. Sacchi Landriani Ā· 1989
Boundary Value Problems of Mathematical Physics (Proceedings of the Steklov Institute of Mathematics,)Ladyzens Ā· 1971- šThe equations of Navier-Stokes and abstract parabolic equationsWolf von Wahl Ā· 1985
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
š Related topics
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