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A note on the generalized energy inequality in the Navier-Stokes equations. (English) Zbl 1099.35099
The authors prove the existence of a suitable weak solution such that the generalized energy inequality is satisfied for all non-negative smooth test functions. The usual definition requires that the test functions must have compact support.
The construction is based on a special approximation which provides smooth solutions and thus the solution itself is an acceptable test function for the approximate problem.

MSC:
35Q35 PDEs in connection with fluid mechanics
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:
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