A note on the generalized energy inequality in the Navier-Stokes equations.
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.
scientific article; zbMATH DE number 5074705