Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces

By Jiahong Wu. 2006

227 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1e9d04e7bab0dc7b4b12695a9d395e7f6bde4b93

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

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.”
Regularity Criteria for the Generalized MHD Equations (2008, background): “The following proposition provides a lower bound for an integral originated from the dissipative term in the process of Lp estimates (see Chen et al., 2007; Wu, 2006).”
A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation (2006, methodology): “If we use the standard energy method as in [5, 26], we need to establish the lower bound for the term generated from the dissipative part ∫”
Global Regularity for a Class of Generalized Magnetohydrodynamic Equations (2011, background): “The following proposition provides a lower bound for an integral originated from the dissipative term in the process of L estimates (see [7,24]).”
The Optimal Decay Estimates on the Framework of Besov Spaces for Generally Dissipative Systems (2014, background): “The first one is the improved Bernstein inequality, see, for example, [27].”
Random Data Cauchy Theory for the Generalized Incompressible Navier–Stokes Equations (2012, methodology): “For the GNS equations, Wu [17] obtained the unique local solution with the initial data u0 ∈ Ḃ p,q, where r = 1 + Np − 2α, 1 < q ≤ ∞, either 12 < α and p = 2 or 12 < α ≤ 1 and 2 < p < ∞, and obtained the unique global solution with the small initial data.”
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.”
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.”
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].”