In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.展开更多
In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.
In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical b...In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.展开更多
We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function s...We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2.The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.展开更多
This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.
In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < <em>α</em> ≤ 2, we prove gl...In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < <em>α</em> ≤ 2, we prove global well-posedness for initial data <img src="Edit_b7b43d4c-00d8-49d6-9066-97151fb5c337.bmp" alt="" /> with 1 ≤ <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞, and analyticity of solutions with 1 < <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞. In particular, we also proved that when <em>α</em> = 1, both <em>u</em> and <img src="Edit_a5af0853-8adc-4a08-b8a2-b9a70ea0f409.bmp" alt="" /> belong to <img src="Edit_03a932cc-aa58-4568-83ad-f16416cc7b71.bmp" alt="" />. We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is <img src="Edit_083986e9-4e1c-4494-ac5d-a7d30a12df97.bmp" alt="" /> as <em>t</em> → ∞.展开更多
This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals t...This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals that the solutions lying in the global attractor are analytic in time with values in a Gevrey class of analytic functions in space.展开更多
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
文摘In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.
基金supported by NSF of China(11422106)the NSF of China(11171261)+1 种基金Fok Ying Tung Education Foundation(151001)supported by“Fundamental Research Funds for the Central Universities”
文摘In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.
基金W.-X.Li's research was supported by NSF of China(11871054,11961160716,12131017)the Natural Science Foundation of Hubei Province(2019CFA007)T.Yang's research was supported by the General Research Fund of Hong Kong CityU(11304419).
文摘We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2.The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.
基金Supported by National Natural Science Foundation of P.R.China
文摘This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.
文摘In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < <em>α</em> ≤ 2, we prove global well-posedness for initial data <img src="Edit_b7b43d4c-00d8-49d6-9066-97151fb5c337.bmp" alt="" /> with 1 ≤ <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞, and analyticity of solutions with 1 < <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞. In particular, we also proved that when <em>α</em> = 1, both <em>u</em> and <img src="Edit_a5af0853-8adc-4a08-b8a2-b9a70ea0f409.bmp" alt="" /> belong to <img src="Edit_03a932cc-aa58-4568-83ad-f16416cc7b71.bmp" alt="" />. We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is <img src="Edit_083986e9-4e1c-4494-ac5d-a7d30a12df97.bmp" alt="" /> as <em>t</em> → ∞.
文摘勃艮第地区(Bourgogne)是法国的骄傲,不仅风景如画而且美酒如云。她是举世公认的著名法定葡萄酒产区,葡萄园根据种植方法、种植葡萄及土壤特性分为大区级产区(Appelations Régionales)、村级产区(Appelations Village)和特级产区(Appellation Grands Crus)。当地整整100个法定产区(AOC),占整个法国葡萄酒法定产区的20%以上。
基金Supported by NSF of China(11971356)NSF of Zhejiang Province(LY17A010011)。
文摘This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals that the solutions lying in the global attractor are analytic in time with values in a Gevrey class of analytic functions in space.
