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The Green’s function of the Navier-Stokes equations for gas dynamics in \(\mathbb R^3\). (English) Zbl 1075.76053
Summary: We derive pointwise estimates for the Green’s function of the Navier-Stokes equations for the compressible fluid. Our analysis shows that the short-time behavior of the Green’s function is dominated by the high-frequency waves but the large-time behavior is dictated by low-frequency waves. Furthermore, the low-frequency waves consist of entropy and acoustic waves that demonstrate a weaker form of Huygens’ principle.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
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