Theory of Function Spaces II

Triebel, Hans

doi:10.1007/978-3-0346-0419-2

Cited by 1,126 publications

(956 citation statements)

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“…Let ( x, y, z) be the selected point in the new coordinates and perform the change of coordinates x = ξ + x , y = η + y z = ζ + z + yξ , which sends the selected point to (0, 0, 0) and hence the manifold in (0, x s , 0). 44 For example choose A(x, y) = x − F (y) + F (ȳ).…”

Section: Finishing the Proofmentioning

confidence: 99%

Exponential Decay of Correlations for Piecewise Cone Hyperbolic Contact Flows

Baladi

Liverani

2012

Commun. Math. Phys.

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Abstract. We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author's version [30] of Dolgopyat's estimates for contact flows and the first author's work with Gouëzel [6] on piecewise hyperbolic discrete-time dynamics.

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Section: Finishing the Proofmentioning

confidence: 99%

Exponential Decay of Correlations for Piecewise Cone Hyperbolic Contact Flows

Baladi

Liverani

2012

Commun. Math. Phys.

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“…Before proving Lemmas 2.1 and 2.3, we first recall the so-called Littlewood-Paley operators and their elementary properties which allow us to define the Besov spaces (see for example [3,4,33,39]). It will be also convenient to introduce some function spaces and review some well-known facts.…”

Section: Casementioning

confidence: 99%

Global Regularity Results of the 2D Boussinesq Equations with Fractional Laplacian Dissipation

2016

J. Math. Fluid Mech.

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As a continuation of the previous work [47], in this paper we focus on the Cauchy problem of the two-dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation. We give an elementary proof of the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. The argument is based on the nonlinear lower bounds for the fractional Laplacian established in [13]. Consequently, this result significantly improves the recent works [13,45,47].

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“…Recall that the classical Besov spaces can also be defined via local polynomial approximation (local oscilations), see e.g. [19]. Furthermore, the anisotropic Besov space from [14,10] are defined via local piecewise polynomial approximation.…”

Section: Anisotropic Besov Spaces (B-spaces)mentioning

confidence: 99%

“…Our B-spaces can be viewed as a generalization of the classical Besov spaces as well as the anisotropic Besov spaces studied by Bownik [1] with weight 1 (see §5.3). For the theory of classical Besov spaces we refer the reader to [16,18,19].…”

Section: Introductionmentioning

confidence: 99%