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Depletion of nonlinearity in the pressure force driving Navier-Stokes flows. (English) Zbl 1312.76013

Summary: The dynamics of the velocity norms \(|\| u\|_{L^q}\) , for \(q\geq 3\), in Navier-Stokes flows are studied. The pressure term that drives these dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between \(|u|\) and \(|\nabla|u||\), among other things. Under viscous effects, such depletion may give rise to mild growth of \(\| u\|_{L^q}\). We explore the possibility of non-singular growth of \(\| u\|_{L^q}\) .

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
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