양민석 교수

Abstract In this paper, we study the potential singular points of interior and boundary suitable weak solutions to the 3D Navier–Stokes equations. It is shown that the upper box dimensions of interior singular points and boundary singular points are bounded by 7/6 and 10/9, respectively. Both proofs rely on the recent progress of -regularity criteria at one scale.

Abstract We establish new Liouville-type theorems for weak solutions of the stationary Navier–Stokes equations, stationary magnetohydrodynamics (MHD) equations and stationary Hall–MHD equations under some conditions on the growth of certain Lebesgue norms of the velocity and the magnetic field.

In this paper we prove a parabolic Triebel–Lizorkin space estimate for the operator given by <disp-formula content-type="math/mathml"> \[ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Superscript alpha Baseline f left-parenthesis t comma x right-parenthesis equals integral Subscript 0 Superscript t Baseline integral Underscript double-struck upper R Superscript d Baseline Endscripts upper P Superscript alpha Baseline left-parenthesis t minus s comma x minus y right-pa