The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial...

mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis...

bounded) at all points in the domain. This is called the Navier–Stokes existence and smoothness problem. The Clay Mathematics Institute has called this...

transfer, and electrical engineering. A proof explaining the properties and bounds of the equations, such as Navier–Stokes existence and smoothness, is one...

establishment of finite time blowup for a modification of the Navier–Stokes existence and smoothness Millennium Problem his 2015 resolution of the Erdős discrepancy...

currently believed to be false, such as NP = co-NP and P = PH. It is also intuitively argued that the existence of problems that are hard to solve but for which...

problems and their resolution in special cases is considered to be a significant advance in the mathematical theory (cf. Navier–Stokes existence and smoothness)...

The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems...

Perelman The Riemann hypothesis Yang–Mills existence and mass gap Navier–Stokes existence and smoothness The Birch and Swinnerton-Dyer conjecture Some of the...

linear case, the existence of a solution of a non-linear system is a difficult problem (cf. Navier–Stokes existence and smoothness.) Other examples of...

mother was working on, the Navier-Stokes existence and smoothness problem. Good Will Hunting (1997) – Janitor and genius Will Hunting (Matt Damon) begins...

1982 work with Luis Caffarelli and Robert Kohn made a seminal contribution to the Navier–Stokes existence and smoothness, in the field of mathematical...

compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2 n {\displaystyle 2n} , so its cohomology groups...

Poincaré's own work, and there was frequent confusion between the notion of a topological manifold, a PL manifold, and a smooth manifold. For this reason...

mathematician. She expressed an interest in solving the Navier-Stokes existence and smoothness problem which her mother was working on. Sammy Fabelman...

Navier–Stokes equations, see section on fluid dynamics Navier–Stokes existence and smoothness Stokes' theorem Kelvin–Stokes theorem Generalized Stokes theorem...

Shankar, Arul (2015). "Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0". Annals...

coherent structure Turbulence kinetic energy Mesocyclones Navier–Stokes existence and smoothness Swing bowling Taylor microscale Turbulence modeling Velocimetry...

Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis Yang–Mills existence and mass...

doi:10.1073/pnas.41.5.312, MR 0070655, PMC 528084, PMID 16589670 Björner, Anders (2011), "A cell complex in number theory", Advances in Applied Mathematics...

about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open...

was the proof of existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the Navier–Stokes equations is one...

Nature Physics Navarro–Frenk–White profile Navier–Stokes equations Navier–Stokes existence and smoothness Navigation mesh Nazir Ahmed (physicist) Naïve...

engineering. Inducement prize contest Space elevator competitions Competitions and prizes in biotechnology Data science competition platform Lists of awards...

evolutionary partial differential equations to the Navier–Stokes equations of fluid mechanics. They found the existence of unique locally defined strong solutions...

as existence, uniqueness, regularity and stability. Among the many open questions are the existence and smoothness of solutions to the Navier–Stokes equations...

1958 to prove the existence and uniqueness of long-time solutions to the Navier–Stokes equations in two spatial dimensions (for smooth enough initial data)...

coupling of the phase separation of the Cahn–Hilliard equation to the Navier–Stokes equations of fluid flow. Allen–Cahn equation Kuramoto–Sivashinsky equation...

equations, the special case of the steady Navier–Cauchy equations given below. Derivation of steady Navier–Cauchy equations in Engineering notation First...

theory of the Navier-Stokes equations. If the Helmholtz projection is applied to the linearized incompressible Navier-Stokes equations, the Stokes equation...