The pointwise estimates of diffusion wave for the Navier-Stokes systems in odd multi-dimensions. (English) Zbl 0912.35122

Liu, Tai-Ping; Wang, Weike

Commun. Math. Phys. 196, No. 1, 145-173 (1998).

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)

MSC:

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

Keywords:

Green function decomposition; Fourier transforms; Green function; wave operator; dissipative operator; generalized Huygens’ principle; decay of coupled nonlinear diffusion waves