On the regularity of the axisymmetric solutions of the Navier-Stokes equations

By Dongho Chae, Jihoon Lee. 2002

117 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/54536233872c101b257854e771cc4a16a811f332

How researchers see this paper

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

In Applied Mathematics

1. Shangkun Weng
2. Zhen Lei
3. Qi S. Zhang
4. Dongyi Wei
5. Dongho Chae
6. Jiahong Wu
7. Peter Constantin
8. Xiaodong Cao

In Control and Systems Engineering

1. Zhen Lei
2. Shangkun Weng
3. Dongyi Wei
4. Qi S. Zhang
5. Dongho Chae
6. Michael Reissig
7. A. Palmieri
8. M. DʼAbbicco

In Mathematical Physics

1. Shangkun Weng
2. Qi S. Zhang
3. Zhen Lei
4. Dongyi Wei
5. Dongho Chae
6. Jiahong Wu
7. A. Palmieri
8. Peter Constantin

Citations in the corpus

• Singularity formation for the incompressible Hall-MHD equations without resistivity (2013, unknown): “(r)r3drdz= Z ∞ −∞ Z ∞ 0 |∇2 y(−∆y) −1Ω|2w(r)r3drdz = C Z |∇2 y(−∆y) −1Ω|2w(r)dy ≤ C Z |Ω|2w(r)dy= Z |Ω|2dx, where w(r) = r−2 and in the last step we have used Lemma 2 in [15]. See also Corollary 2 in [3] for a similar weighted estimate for a singular integral operator. Similarly, we also have Z |∇ 2”
• Liouville type theorems for the steady axially symmetric Navier-Stokes and magnetohydrodynamic equations (2015, methodology): “C5 Z R5 |Ω|2w(r)dy = C5 Z R3 |Ω|2dx, (2.28) where w(r) = r−2 and in the last step we have used the boundedness of Riesz operators in weighted Sobolev spaces (Lemma 2 in [12]). See also Corollary 2 in [4] for a similar weighted estimate for a singular integral operator. Similarly, we also have Z R3 |”
• A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations (2010, background): “Lee [3] who prove regularity results assuming finiteness of another zero dimensional integral.”
• Regularity Criterion to the axially symmetric Navier-Stokes Equations (2015, background): “1 in section 2 to obtain∇ ur r ∈ L(0, T ;L(2)(R(3))), and ur r ∈ L(0, T ;L(6)(R(3))), then the results in [1] or [6] imply the global regularity.”
• Criticality of the Axially Symmetric Navier-Stokes Equations (2015, unknown): “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∞ .”