Two New Regularity Criteria for the 3D Navier-Stokes Equations via Two Entries of the Velocity Gradient Tensor

Regularity criteria for weak solutions of the Magneto-micropolar equations

“…Further results related to the current paper are in [2,21]. The papers [14] and [18] (see also [3,8,12,13,15,17,19,20,22,23,24,28,29]), raised our interest to obtain regularity criteria for weak solutions of the magnetomicropolar system (1), which involve only one component of the velocity field u.…”

A Remark on the Regularity Criterion for the 3D Boussinesq Equations Involving the Pressure Gradient

“…The regularity of its weak solutions and the existence of global strong solutions are challenging open problems; see [1][2][3]. Starting with [4,5], there have been a lot of literature devoted to finding sufficient conditions to ensure the smoothness of the solutions; see [6][7][8][9][10][11][12][13][14][15] and the references cited therein. Since the convective terms are similar in the Navier-Stokes equations and Boussinesq equations, the authors also consider the regularity conditions for (1); see [16][17][18][19][20] and so forth.…”

Some Regularity Criteria for the 3D Boussinesq Equations in the ClassL20,T;B˙∞,Zhang1 2014ISRN Applied MathematicsSelf Cite7010View full textAdd to dashboardCite

“…The regularity of its weak solutions and the existence of global strong solutions are challenging open problems; see [1][2][3]. Initialed by [4,5], there have been a lot of literatures devoted to finding sufficient conditions to ensure the smoothness of the solutions; see [6][7][8][9][10][11][12][13][14][15][16][17][18] and so forth. Since the convective terms are similar in Navier-Stokes equations and Boussinesq equations, the authors also consider the regularity conditions for (1); see [19][20][21][22][23] and so forth.…”