The Maximum Principle and the Global Attractor for the Dissipative 2D Quasi-Geostrophic Equations

By Ning Ju. 2005

249 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/7b9fbf708d1e414180ee2cfe622047a5bc1a2c04

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Exploding solutions for a nonlocal quadratic evolution problem (2010, result): “The following pointwise estimate for fractional derivatives is proved in[13] and represents an improvement of an earlier estimate by Córdoba and Córdoba [11].”
Qualitative properties of solutions to a time-space fractional evolution equation (2012, unknown): “3 in [16]), in dimension N ≥ 1 where δ ∈ [0, 2] and q ≥ 1, for all nonnegative Schwartz functions ψ (in the general case) (−Δ)ψ ≤ qψq−1(−Δ)δ/2ψ.”
A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation (2006, background): “(3.15) Proof: The proof can be found in [ 18 ].”
Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces (2006, unknown): “Ju proved in [14] that if p ≥ 0 and f is, in addition, nonnegative, then (p + 1) f (x) (− )f (x) ≥ (− )f p+1(x).”
Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces Lp or $$\dot{H}^{-1/2}$$ (2007, background): “In this section we give a new proof of the maximum principle property [2, 10 , 5]; we have the following inequality:”
Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation (2007, background): “Recently this problem has attracted a significant amount of research ([1],[2],[3],[4],[5],[6],[9], [11],[12],[13],[14],[17],[18],[19],[20], [21],[22],[23]).”
Refined blowup criteria and nonsymmetric blowup of an aggregation equation (2009, unknown): “Now (19) follows immediately by observing that 0 < α 2 , β 2 , γ 2 < π 2 .”
Long Time Dynamics of Forced Critical SQG (2013, unknown): “[Ju05] N. Ju.”
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]).”
Semilinear structural damped waves (2012, unknown): “, the functional method to close the gap. Proof. The key tool for applying test function method with pseudo-diﬀerential operators like (−△)σ is the following result in Prop.2.3 of [CC] or Prop.3.3 of [J]. It is also used in [FK]. This result gives (−△)σφℓ ≤ ℓφℓ−1(−△)σφ (102) for all σ∈ (0,1] and ℓ≥ ”