Global Well-Posedness in the Super-Critical Dissipative Quasi-Geostrophic Equations

By Dongho Chae, Jihoon Lee. 2003

161 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/971717194c531759da887509e5d27955e29e67c8

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics (2013, unknown): “, see [4] and references therein).”
Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations (2007, background): “Recently this problem has attracted a significant amount of research ([2],[3],[4],[5],[6],[7],[11], [13],[14],[15],[18],[19],[20],[21], [22],[23]).”
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation (2006, background): “In both the critical case and supercritical cases, Chae and Lee considered in [3] the well-posedness of solutions with initial conditions small in Besov spaces (see also Wu [16]).”
The generalized incompressible Navier-Stokes equations in Besov spaces (2004, methodology): “Besov spaces include many of the frequently-used function spaces such as the Sobolev spaces and the Hölder spaces and constitute a very natural setting for studying solutions of various partial differential equations ([1],[4],[5],[7],[12],[13],[15]).”
A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation (2006, methodology): “our result improves the results of [ 5 ] and [17].”
Existence and Uniqueness of the Solution to the Dissipative 2D Quasi-Geostrophic Equations in the Sobolev Space (2004, background): “Notice that our results in the Sobolev space H s (R 2 ) and those of [ 1 ] and [22] in the”
Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space (2006, methodology): “As is pointed out in [2], we have difficulty to find an appropriate space E which yields the following continuous bilinear estimate of the Duhamel term: ∥ ∥ ∥ ∥ ∫ ·”
Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation (2006, unknown): “[8] Chae, D. and Lee, J.; Global well-posedness in the super-critical dissipative quasi-geostrophic equations, Comm. Math.”
The Maximum Principle and the Global Attractor for the Dissipative 2D Quasi-Geostrophic Equations (2005, background): “See, among others, Berselli, [2] Chae and Lee [ 3 ], Constantin, D. Cordoba and Wu [4], Constantin, Majda and Tabak [7], Constantin and Wu [8], D. Cordoba [9], A. Cordoba and D. Cordoba [10, 11], D. Cordoba and Fefferman [12], Ju [16], Ju [17], Majda and Tabak [22], Ohkitani et al [23], Resnick [25]”
Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation (2007, background): “Recently this problem has attracted a significant amount of research ([1–6,9,11–15,18–24]).”
On the global regularity for the supercritical SQG equation (2014, result): “γ is bounded uniformly from above for γ ∈ [γ0,3/2], so that the dependence on γ will be dropped. We will make use of the interpolation inequality kfk2 H˙σ ≤ Ckfk 2−σ L2 kfk σ H˙2, (4.3) valid for σ ∈ [0,2], with constant C independent of σ. Lastly we shall use that kR⊥kLp→Lp ≤ Cp for p ≥ 2, with C &”