zbMATH — the first resource for mathematics

The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions. (English) Zbl 0912.35122
The paper deals with time-asymptotic behaviour of solutions to isentropic Navier-Stokes equations in odd multi-dimensions (the more difficult case of even space dimensions is left to the future. First, using Fourier transforms, the authors obtain pointwise estimates for the Green function of the Navier-Stokes system linearized about a constant state. To this end, they decompose the Green function into two parts corresponding to the wave operator and to the dissipative operator, respectively. The results are then interpreted as a generalized Huygens’ principle, and are applied to study the decay of coupled nonlinear diffusion waves.
Reviewer: O.Titow (Berlin)

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI