NavierStokesGesetze

The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances, such as liquids and gases. In the Navier-Stokes equations, the dynamic behavior of fluids is governed by two main components: the conservation of mass (continuity equation) and the conservation of momentum (Navier-Stokes equation).

The equations describe a fluid's velocity and pressure as a function of time and space, and are named after the French mathematicians Claude-Louis Navier and George Gabriel Stokes. The Navier-Stokes equations are a combination of the continuity equation, which states that the fluid's mass is conserved, and the Navier-Stokes equation, which describes the relationship between the fluid's momentum, stress, and rate of strain.

The Navier-Stokes equations are based on several fundamental principles: the Cauchy's equation, which describes the acceleration of an arbitrary fluid particle in terms of its velocity and pressure; the strain-stress relationship, which relates the rate of deformation of the fluid to the forces acting upon it; and the continuity equation, which states that the fluid's mass is conserved.

The Navier-Stokes equations have numerous applications in various fields, such as civil engineering, oceanography, meteorology, and aerodynamics. They are used to model and predict various phenomena, including ocean currents, atmospheric circulation, and the flow of fluids in pipes and channels.

In recent years, solving the Navier-Stokes equations has become increasingly complex, and solvingthem for all time and space remains an open problem in mathematics. However, numerical methods have been developed to solve the equations approximately, allowing for the simulation of a wide range of fluid dynamic phenomena.