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. For example, the Navier–Stokes equations are often used to model fluid flows that are turbulent, which means that the fluid is highly chaotic and unpredictable. Turbulence is a difficult phenomenon to model and understand, and it adds another layer of complexity to the problem of solving the Navier–Stokes equations. To solve the Navier–Stokes equations, we need to find a velocity field v ( x , t ) and a pressure field p ( x , t ) that satisfy the equations and the given boundary conditions. This can be done using a variety of numerical techniques, such as finite element methods, spectral methods, or finite difference methods.