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Zero Mach number limit for compressible flows with periodic boundary conditions. (English) Zbl 1048.35075
The author studies the convergence to incompressible Navier-Stokes flows of slightly compressible viscous flows with ill-prepared initial data and periodic boundary conditions. For arbitrarily large initial data, it is shown that the compressible flow with small Mach number exists as long as the incompressible one does. In particular, it exists globally if the corresponding incompressible solution exists for all time. The author also treats small initial data with critical regularity and proves for them the global convergence in the small. The proof is based on a priori estimates, Littlewood-Paley decomposition technique, and on some theorems from harmonic analysis.

MSC:
35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
42B25 Maximal functions, Littlewood-Paley theory
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