Abstract
Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of satisfying the strong energy inequality. Extending previous results Farwig et al., Journal of Mathematical Fluid Mechanics, 2007, to appear we prove among other things that u is regular if either the kinetic energy or the dissipation energy is (left-side) HOlder continuous as a function of time t with HOlder exponent and with sufficiently small HOlder seminorm. The proofs use local regularity results which are based on the theory of very weak solutions and on uniqueness arguments for weak solutions.
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