Search results
Results From The WOW.Com Content Network
However, theoretical understanding of their solutions is incomplete, despite its importance in science and engineering. For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proven that smooth solutions always exist. This is called the Navier–Stokes existence and smoothness problem.
This term makes the Navier–Stokes equations highly sensitive to initial conditions, and it is the main reason why the Millennium Prize conjectures are so challenging. In addition to the mathematical challenges of solving the Navier–Stokes equations, there are also many practical challenges in applying these equations to real-world situations.
The Navier–Stokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades ...
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five years) for a notable research work in analysis that has appeared during the past six years.
Olga Aleksandrovna Ladyzhenskaya (Russian: Ольга Александровна Ладыженская, IPA: [ˈolʲɡə ɐlʲɪˈksandrəvnə ɫɐˈdɨʐɨnskəɪ̯ə] ⓘ; 7 March 1922 – 12 January 2004) was a Russian mathematician who worked on partial differential equations, fluid dynamics, and the finite-difference method for the Navier–Stokes equations.
Caffarelli published "The regularity of free boundaries in higher dimensions" in 1977 in Acta Mathematica. [8] One of his most cited results regards the Partial regularity of suitable weak solutions of the Navier–Stokes equations; it was obtained in 1982 in collaboration with Louis Nirenberg and Robert V. Kohn.
This equation is called the mass continuity equation, or simply the continuity equation. This equation generally accompanies the Navier–Stokes equation. In the case of an incompressible fluid, Dρ / Dt = 0 (the density following the path of a fluid element is constant) and the equation reduces to:
The Navier-Stokes equations were developed in the early 1800s to model the physics of fluid mechanics. Jean Leray, in a seminal achievement in the 1930s, formulated an influential notion of weak solution for the equations and proved their existence. [19] His work was later put into the setting of a boundary value problem by Eberhard Hopf. [20]