Blow Ups of Complex Solutions of the 3D-Navier-Stokes System and Renormalization Group Method

Blow Ups of Solutions of the 3 − D Navier - Stokes System Ya

Logarithmically Improved Blow-up Criteria for the 3d Nonhomogeneous Incompressible Navier-stokes Equations with Vacuum

This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes equations in space dimension three. By making use of the “weakly nonlinear” energy estimate approach introduced by Lei and Zhou in [16], we establish two logarithmically improved blow-up criteria of the strong or smooth solutions subject to vacuum for the 3D nonhomogeneous incompressible Navier-Stokes equati...

Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations

Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments...

A note on necessary conditions for blow-up of energy solutions to the Navier-Stokes equations

In the present note, we address the question about behavior of L3-norm of the velocity field as time t approaches blow-up time T . It is known that the upper limit of the above norm must be equal to infinity. We show that, for blow-ups of type I, the lower limit of L3-norm equals to infinity as well. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

Global regularity of solutions to systems of reaction-diffusion with Sub-Quadratic Growth in any dimension

This paper is devoted to the study of the regularity of solutions to some systems of reaction– diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension N . The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It al...