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Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations. (English) Zbl 1154.35070

Summary: We prove that the smooth solutions to the Cauchy problem for the Navier-Stokes equations with conserved total mass, finite total energy and finite momentum of inertia lose the initial smoothness within a finite time in the case of space dimension 3 or greater even if the initial data are not compactly supported. The cases of isentropic and incompressible fluids are also considered.

MSC:

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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