On the Smallness of the (possible) Singular Set in Space for 3d Navier-stokes Equations
نویسنده
چکیده
We utilize L∞ estimates on the complexified solutions of 3D Navier-Stokes equations via a plurisubharmonic measure type maximum principle to give a short proof of the fact that the Hausdorff dimension of the (possible) singular set in space is less or equal 1 assuming chaotic, Cantor set-like structure of the blow-up profile.
منابع مشابه
On the Partial Regularity of a 3D Model of the Navier-Stokes Equations
We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the ...
متن کاملLp-SOLUTIONS OF THE STEADY-STATE NAVIER–STOKES WITH ROUGH EXTERNAL FORCES
In this paper we address the existence, the asymptotic behavior and stability in L and L, 3 2 < p ≤ ∞, for solutions to the steady state 3D Navier-Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier-Stokes equations in L spaces, and we prove the stability of these soluti...
متن کاملL-Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces
In this paper we address the existence, the asymptotic behavior and stability in L and L , 3 2 < p ≤ , for solutions to the steady state 3D Navier–Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier–Stokes equations in L spaces, and we prove the stability of these soluti...
متن کاملProbabilistic Analysis of Singularities for the 3d Navier-stokes Equations
The classical result on singularities for the 3D Navier-Stokes equations says that the 1-dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time t, with probability one the set of singular points is empty. The same result is true for a.e. initial condition wit...
متن کاملRegularity of Forward-in-time Self-similar Solutions to the 3d Navier-stokes Equations
Any forward-in-time self-similar (localized-in-space) suitable weak solution to the 3D Navier-Stokes equations is shown to be infinitely smooth in both space and time variables. As an application, a proof of infinite space and time regularity of a class of a priori singular small self-similar solutions in the critical weak Lebesgue space L3,∞ is given.
متن کامل