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Time analyticity and backward uniqueness of weak solutions of the Navier-Stokes equations of multidimensional compressible flow. (English) Zbl 1387.35454

Summary: We prove that solutions of the Navier-Stokes equations of three-dimensional compressible flow, restricted to fluid-particle trajectories, can be extended as analytic functions of complex time. As consequences we derive backward uniqueness of solutions as well as sharp rates of smoothing for higher-order Lagrangean time derivatives. The solutions under consideration are in a reasonably broad regularity class corresponding to small-energy initial data with a small degree of regularity, the latter being required for conversion to the Lagrangean coordinate system in which the analysis is carried out.

MSC:

35Q30 Navier-Stokes equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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