Renormalization group method. Application to Navier-Stokes equation. (English) Zbl 1021.76009
Summary: The aim is to present a rather unusual and partly heuristic application of the renormalization group theory to Navier-Stokes equations with space-periodic boundary conditions. We obtain in this way a new nonlinear renormalized equation with a nonlinear term which is invariant under Stokes operator. Its relation to Navier-Stokes equations is investigated for non-resonant domains.
MSC:
76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
35Q30 | Navier-Stokes equations |
37L99 | Infinite-dimensional dissipative dynamical systems |