About the Regularized Navier–Stokes Equations
By Marco Cannone, Grzegorz Karol Karch. 2003
53 citations recorded by the source corpus.
Abstract.The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier–Stokes system. The Marcinkiewicz space L3,∞ is used to prove some asymptotic stability results for solutions with infinite energy. Next, this approach is applied to the analysis of two classical “regularized” Navier–Stokes systems. The first one was introduced by J. Leray and consists in “mollifying” the nonlinearity. The second one was proposed by J.-L. Lions, who added the artificial hyper-viscosity (−Δ)ℓ/ 2, ℓ > 2 to the model. It is shown in the present paper that, in the whole space, solutions to those modified models converge as t → ∞ toward solutions of the original Navier–Stokes system.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5d6aed071c7122ec4a507df9a05489905da041f7
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
- Baoquan Yuan
- Changxing Miao
- Marco Cannone
- Grzegorz Karol Karch
- Bo Zhang
- Juan Luis V'azquez
- Zhen Lei
- Dongho Chae
In Control and Systems Engineering
- Baoquan Yuan
- Changxing Miao
- Marco Cannone
- Grzegorz Karol Karch
- Bo Zhang
- Jiaowan Luo
- Ryo Ikehata
- Kenji Nishihara
In Mathematical Physics
- Marco Cannone
- Grzegorz Karol Karch
- Baoquan Yuan
- Changxing Miao
- Juan Luis V'azquez
- Ryo Ikehata
- Kenji Nishihara
- Zhen Lei
Citations in the corpus
- Smooth or singular solutions to the Navier-Stokes system ? (2002, background): “However, there exist two exceptions, more exactly two critical spaces where Kato’s method applies with just one norm: the Lorentz space L3;N (considered independently by Yamazaki [34] and by Meyer [30], and devoloped recently in [5]) and the pseudomeasure space of Le Jan and Sznitman [26] (see [8]).”
- Well-posedness of the Cauchy problem for the fractional power dissipative equation in critical Besov spaces (2008, unknown): “For the generalized Navier–Stokes equation, see [2,32].”
- Well-posedness of the Cauchy problem for the fractional power dissipative equations (2006, background): “Concerning the generalized Navier-Stokes equations, please refer to [3].”