The paper claims a pressure norm can guarantee smooth Navier-Stokes solutions, but the central bound is not proven and the system is not shown to be equivalent to Navier-Stokes.
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Functional Reformulation of the Continuity Equation in Gases with Constant Density and its Application to the Existence Problem of Smooth Solutions to the Navier Stokes System
The paper claims a pressure norm can guarantee smooth Navier-Stokes solutions, but the central bound is not proven and the system is not shown to be equivalent to Navier-Stokes.