Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier-Stokes Equations II

Lower bounds on blow up solutions of the three-dimensional Navier–Stokes equations in homogeneous Sobolev spaces

Lower Bound on the Blow-up Rate of the Axisymmetric Navier–Stokes Equations

Chiun-Chuan Chen1, Robert M. Strain2, Horng-Tzer Yau2, and Tai-Peng Tsai3 1Department of Mathematics and Taida Institute of Mathematical Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106 and National Center for Theoretical Sciences, Taiwan, Taipei Office. 2Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA, and 3Depar...

EFFECT OF TIME-DEPENDENT TRANSPIRATION ON AXISYMMETRIC STAGNATION-POINT FLOW AND HEATTRANSFER OF A VISCOUS FLUID ON A MOVING CIRCULAR CYLINDER

Effect of time dependent normal transpiration on the problem of unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder moving simultaneously with time-depended angular and axial velocities and with time-dependent wall temperature or wall heat flux are investigated. The impinging free stream is steady with a strain rate . A re...

Regularity of Leray-hopf Solutions to Navier-stokes Equations (ii)–blow up Rate with Small L(r) Data

where u and p denote the unknown velocity and pressure of incompressible fluid respectively. In this paper, we estimate the upper bound of blow up rate for the Navier-Stokes equations. Main Theorem. There is δ > 0 such that if ‖u0‖L2(R3) ≤ δ, and if u is a LerayHopf solution to the problem (1.1) and blow up at t = T , then for any small ǫ > 0, there is t0 ∈ (0, T ), such that (1.2) ‖u(t)‖L∞(R3)...

Finite Time Blow-up of a 3D Model for Incompressible Euler Equations

We investigate the role of convection on its large time behavior of 3D incompressible Euler equations. In [15], we constructed a new 3D model by neglecting the convection term from the reformulated axisymmetric Navier-Stokes equations. This model preserves almost all the properties of the full Navier-Stokes equations, including an energy identity for smooth solutions. The numerical evidence pre...