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- Navier%E2%80%93Stokes_existence_and_smoothness abstract "The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, one of the pillars of fluid mechanics (such as with turbulence). These equations describe the motion of a fluid (that is, a liquid or a gas) in space. Solutions to the Navier–Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete. In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering.Even much more basic properties of the solutions to Navier–Stokes have never been proven. For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proved that smooth solutions always exist, or that if they do exist, they have bounded energy per unit mass. This is called the Navier–Stokes existence and smoothness problem.Since understanding the Navier–Stokes equations is considered to be the first step to understanding the elusive phenomenon of turbulence, the Clay Mathematics Institute in May 2000 made this problem one of its seven Millennium Prize problems in mathematics. It offered a US$1,000,000 prize to the first person providing a solution for a specific statement of the problem: Prove or give a counter-example of the following statement:In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.".
- Navier%E2%80%93Stokes_existence_and_smoothness wikiPageExternalLink why-global-regularity-for-navier-stokes-is-hard.
- Navier%E2%80%93Stokes_existence_and_smoothness wikiPageExternalLink 18185364.
- Navier%E2%80%93Stokes_existence_and_smoothness wikiPageExternalLink navier%E2%80%93stokes-equation.
- Navier%E2%80%93Stokes_existence_and_smoothness wikiPageID "6013654".
- Navier%E2%80%93Stokes_existence_and_smoothness wikiPageRevisionID "644456602".
- Navier%E2%80%93Stokes_existence_and_smoothness hasPhotoCollection Navier–Stokes_existence_and_smoothness.
- Navier%E2%80%93Stokes_existence_and_smoothness subject Category:Fluid_dynamics.
- Navier%E2%80%93Stokes_existence_and_smoothness subject Category:Millennium_Prize_Problems.
- Navier%E2%80%93Stokes_existence_and_smoothness subject Category:Partial_differential_equations.
- Navier%E2%80%93Stokes_existence_and_smoothness subject Category:Unsolved_problems_in_mathematics.
- Navier%E2%80%93Stokes_existence_and_smoothness comment "The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, one of the pillars of fluid mechanics (such as with turbulence). These equations describe the motion of a fluid (that is, a liquid or a gas) in space. Solutions to the Navier–Stokes equations are used in many practical applications. However, theoretical understanding of the solutions to these equations is incomplete.".
- Navier%E2%80%93Stokes_existence_and_smoothness label "Existência e suavidade de Navier-Stokes".
- Navier%E2%80%93Stokes_existence_and_smoothness label "Navier–Stokes existence and smoothness".
- Navier%E2%80%93Stokes_existence_and_smoothness label "Существование и гладкость решений уравнений Навье — Стокса".
- Navier%E2%80%93Stokes_existence_and_smoothness label "ナビエ-ストークス方程式の解の存在と滑らかさ".
- Navier%E2%80%93Stokes_existence_and_smoothness sameAs m.0fkm5k.
- Navier%E2%80%93Stokes_existence_and_smoothness wasDerivedFrom Navier–Stokes_existence_and_smoothness?oldid=644456602.
- Navier%E2%80%93Stokes_existence_and_smoothness isPrimaryTopicOf Navier–Stokes_existence_and_smoothness.