Well-posedness of quasi-geostrophic equations with data in Besov- spaces

Li, Pengtao; Yang, Qixiang

doi:10.1016/j.na.2013.08.021

Cited by 11 publications

(8 citation statements)

References 34 publications

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“…The limit case p = ∞ was completely tackled by Abidi and Hmidi [1] and Wang and Zhang [48], respectively. For more interesting results related to this topic, we refer the reader to see [3,14,16,22,39,46].…”

Section: Surface Quasi-geostrophic Equationmentioning

confidence: 99%

The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces

Zhao

2016

Journal of Mathematical Physics

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In this paper, we first generalize a new energy approach, developed by Y. Guo and Y. Wang [27], in the framework of homogeneous Besov spaces for proving the optimal temporal decay rates of solutions to the fractional power dissipative equation, then we apply this approach to the supercritical and critical quasi-geostrophic equation and the critical Keller-Segel system. We show that the negative Besov norm of solutions is preserved along time evolution, and obtain the optimal temporal decay rates of the spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

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Section: Surface Quasi-geostrophic Equationmentioning

confidence: 99%

The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces

Zhao

2016

Journal of Mathematical Physics

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“…These spaces have been applied to the study of non‐linear PDE. See Li and Yang , Lin and Yang , Liang et al . , Yang and Yuan and Yuan et al .…”

Section: Besov Type Spaces Via Wavelets On Double-struckhdmentioning

confidence: 99%

“…In recent years, such wavelet characterizations of Besov type spaces have been applied to the nonlinear problems in fluid equations. See Lin and Yang , Li and Yang and Li et al . .…”

Section: Introductionmentioning

confidence: 99%

Regular orthogonal basis on Heisenberg group and application to function spaces

Yang

2014

Math Methods in App Sciences

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In this paper, we construct some compactly supported orthogonal regular wavelet basis on Heisenberg group H d . Because of the regularity of wavelets, we could use such wavelets to characterize function spaces on H d , such as bounded mean oscillation space (BMO) space, Hardy space, Besov spaces and Besov-Morrey spaces.where S.z, z 0 / D 2Q szN z 0 is the symplectic inner product (or symplectic form). Alternatively, by the real coordinates, the aforementioned multiplication can be represented as .x, y, t/.x 0 , y 0 , t 0 / D .x C x 0 , y C y 0 , t C t 0 C 2.y 0 x x 0 y//, (2.2)

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“…Since Kato-Fujita find mild solution for Navier-Stokes equations (1.1), there are many works which considered the mild solution. See [5,6,11,13,15,17,19,21,22,23,24,25,26,32,33,34,35,36,37,38,41,42]. Among all the known results, Koch-Tataru proved the well-posedness of BMO −1 in 2001.…”

Section: Introductionmentioning

confidence: 97%

Navier-Stokes equations, symmetric and uniform analytic solutions in phase space

Yang¹

2018

Preprint

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For incompressible Navier-Stokes equations, Necas-Ruzicka-Sverak proved that selfsimilar solution has to be zero in 1996. Further, Yang-Yang-Wu find symmetry property plays an important role in the study of ill-posedness. In this paper, we consider two types of symmetry property. We search special symmetric and uniform analytic functions to approach the solution and establish global uniform analytic and symmetric solution with initial value in general symmetric Fourier-Herz space. For two kinds of symmetry of initial data, we prove that the solution has also the same symmetric structure. Further, we prove that the uniform analyticity is equivalent to the convolution inequality on Herz spaces. By these ways, we can use symmetric and uniform analytic functions to approximate the solution.

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Well-posedness of quasi-geostrophic equations with data in Besov- spaces

Cited by 11 publications

References 34 publications

The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces

The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces

Regular orthogonal basis on Heisenberg group and application to function spaces

Navier-Stokes equations, symmetric and uniform analytic solutions in phase space

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