Tran, Chuong V.; Yu, Xinwei Depletion of nonlinearity in the pressure force driving Navier-Stokes flows. (English) Zbl 1312.76013 Nonlinearity 28, No. 5, 1295-1306 (2015). 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 \(\| u\|_{L^q}\) . Cited in 4 Documents MSC: 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:Navier-Stokes equations; depletion of nonlinearity; global regularity PDFBibTeX XMLCite \textit{C. V. Tran} and \textit{X. Yu}, Nonlinearity 28, No. 5, 1295--1306 (2015; Zbl 1312.76013) Full Text: DOI