The generalized incompressible Navier-Stokes equations in Besov spaces

By Jiahong Wu. 2004

95 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/221e6055ae5912ae06a997fed219225b5857d138

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In Applied Mathematics

In Computational Mechanics

In Mathematical Physics

Citations in the corpus

Fractional Gagliardo–Nirenberg and Hardy inequalities under Lorentz norms (2012, background): “They play a crucial role in the study of many important PDEs [1–11], among them the quasi-geostrophic equation in geophysical fluid dynamics [12], which is crucial to the understanding of atmosphere and ocean, as well as being an enlightening model of 3D Euler equations and Navier–Stokes equations.”
Global well-posedness for a Boussinesq- Navier-Stokes System with critical dissipation (2009, background): “1) is reduced to the generalized Navier-Stokes system which was studied in a series of papers [24, 25, 26] for all space dimension d ≥ 2.”
On the Regularity Conditions for the Navier-Stokes and Related Equations (2005, methodology): “We also remark that more recently there were studies on the small data global well-posedness on the same equation with 0 ≤ α ≤ 2 by the author of this paper, using the scale invariant Besov spaces ([14]) (see also [33, 7] for related studies).”
Well‐posedness for fractional Navier–Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn) (2012, background): “For the important case ˇ < 1 2 C n 4 , Wu in [22, 23] considered the existence of solution to Equation (1.”
Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces (2006, result): “These results for the GNS equations together with those in [4, 8, 9, 17–20] contribute significantly to understanding how the general fractional dissipation effects the regularity of solutions to dissipative partial differential equations.”