An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier—Stokes Equations

69 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Criticality of the Axially Symmetric Navier-Stokes Equations (2015, background): “3) is that smooth solutions of the axi-symmetric Navier-Stokes equations satisfy the following maximum principle (see, for instance, [2, 7, 3, 20, 21]): sup t ‖Γ(t, ·)‖L∞ ≤ ‖Γ0‖L∞ .”
A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations (2010, background): “Pokorny [24], proving the regularity of one component (either v or v ) implies regularity of the other components of the solution.”
Lower Bound on the Blow-up Rate of the Axisymmetric Navier-Stokes Equations (2007, unknown): “Neustupa–Pokorný [25, 26] proved regularity assuming the zero-dimensional condition vr ∈ Lt Lx with 3/q + 2/s = 1, 3 < q ≤ ∞.”
Regularity Criterion to the axially symmetric Navier-Stokes Equations (2015, methodology): “Here global regularity means T ∗ = +∞, and we only need to prove Ω ∈ L(0, T ;L(2)(R(3))), hence we can use the results in [4] or [14] to obtain global regularity.”
On the Interior Regularity of Suitable Weak Solutions to the Navier–Stokes Equations (2007, methodology): “Following the method in Neustupa and Pokorný (2000), we set u = v− V , where V satisfies divV = v · .”