Depletion of nonlinearity in the pressure force driving Navier–Stokes flows. (17th April 2015)

• Record Type: Journal Article
• Authors: Tran, Chuong V; Yu, Xinwei
• Is Part Of: Nonlinearity. Volume 28:Number 5(2015:May)
• Page Start: 1295
• Page End: 1306
• Publication Date: 2015-04-17
• Subjects: Navier–Stokes equations -- depletion of nonlinearity -- global regularity; 76D03 -- 76D05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/5/1295
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: The dynamics of the velocity norms, for q ⩾ 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 |∇| u ‖, among other things. Under viscous effects, such depletion may give rise to mild growth of . We explore the possibility of non-singular growth of .