| Popis: |
The Navier-Stokes equations appear as a singular perturbation of the Euler equations in which the small parameter ɛ is the viscosity or inverse of the Reynolds number. In many cases the convergence of the solutions of the Navier-Stokes equations to those of the Euler equations remains an outstanding open problem of mathematical physics. The result is not known in the case of the no-slip boundary condition, even in space dimension 2 for which the existence, uniqueness, and regularity of solution for all time is known for both the Navier-Stokes and Euler equations; see, e.g., [Kat84, Kat86, FT79, Tem75, Tem76, Tem01]. Fortunately, and this is the object of Chapters 6 and 7, this problem has been solved in a number of particular situations: special symmetries or boundary conditions other than the no-slip boundary condition. |
