On the Deformation Tensor Regularity for the Navier–Stokes Equations in Lorentz Spaces

This paper is concerned with the regularity criteria in terms of the middle eigenvalue of the deformation (strain) tensor $$\mathcal {D}(u)$$ to the 3D Navier–Stokes equations in Lorentz spaces. It is shown that a Leray–Hopf weak solution is regular on (0, T] provided that the norm $$\Vert \lambda _{2}^{+}\Vert _{L^{p,\infty }(0,T; L ^{q,\infty }(\mathbb {R}^{3}))} $$ with $$ {2}/{p}+{3}/{q}=2$$ $$( {3}/{2}

Keywords:

• Navier–Stokes equations
• Lorentz transformation
• Classical mechanics
• Mathematics
• deformation tensor

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