- #1
Winzer
- 598
- 0
What does it take to look at the well poseness problem of the Navier stokes equations?
Besides knowledge in PDEs.
Besides knowledge in PDEs.
Cool. It's agreed that if you solve this we'll split the $$$.matematikawan said:I could win $1 million if I can solve this.
http://www.claymath.org/millennium/ [Broken]
The Navier-Stokes Equations are a set of partial differential equations that describe the motion of a fluid. They take into account factors such as viscosity, density, and pressure to determine the velocity and pressure fields of a fluid at any given point in space and time.
The Navier-Stokes Equations are important in the study of fluid mechanics and are widely used in engineering and scientific applications. They provide a fundamental understanding of how fluids behave and can be used to solve a variety of problems, from predicting the flow of air around an airplane wing to simulating ocean currents.
The Navier-Stokes Equations were first developed independently by French engineer Claude-Louis Navier and Irish mathematician George Gabriel Stokes in the 19th century. However, the equations were later modified and simplified by German mathematician and physicist Hermann von Helmholtz.
The Navier-Stokes Equations are based on certain assumptions, such as the fluid being incompressible and the flow being steady and laminar. In reality, fluids can exhibit turbulent and unsteady behavior, which the equations cannot accurately model. Additionally, the equations are only valid for Newtonian fluids and do not take into account non-Newtonian behavior.
The Navier-Stokes Equations can be solved analytically for simple cases, but in most practical applications, they are solved numerically using computational fluid dynamics (CFD) methods. This involves breaking the equations down into discrete elements and solving them using algorithms and computer simulations.