A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

Details A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

2008-03-13

arxiv.org/abs/0803.2057v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

10.1007/s10884-008-9124-3

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that
belongs to the class $L^3L^{9/2}$ and $\n u$ belongs to $L^3L^{9/5}$ localy
away from a 1/2-H\"{o}lder continuous curve in time satisfies the generalized
energy equality. In particular every such solution is suitable.

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