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Approximation of a simple Navier-Stokes model by monotonic rearrangement

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  • We consider the very simple Navier-Stokes model for compressible fluids in one space dimension, where there is no temperature equation and both the pressure and the viscosity are proportional to the density. We show that the resolution of this Navier-Stokes system can be reduced, through the crucial intervention of a monotonic rearrangement operator, to the time discretization of a very elementary differential equation with noise. In addition, our result can be easily extended to a related Navier-Stokes-Poisson system.
    Mathematics Subject Classification: 35Q30, 35Q35.


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