Trudinger–Moser type inequalities with logarithmic weights in fractional dimensions
Advanced Nonlinear StudiesThe purpose of this paper is two-fold. First, we derive sharp Trudinger–Moser inequalities with logarithmic weights in fractional dimensions: sup∫01w(r)u′(r)β+2dλα1/(β+2)≤1∫01eμα,θ,γuβ+2β+11−γdλθ 1 and γ = 1 are also be considered in this part to ...
Xue Jianwei, Zhang Caifeng, Zhu Maochun
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Local and Global Existence of Strong Solutions to Large Cross Diffusion Systems
Advanced Nonlinear Studies, 2018 We study the solvability of a general class of cross diffusion systems and establish the local and global existence of their strong solutions under the weakest assumption that they are VMO.
Le Dung
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Besov regularity for solutions of p-harmonic equations
Advances in Nonlinear Analysis, 2017 We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., div𝒜(x,Du)=divF,{\operatorname{div}\mathcal{A}(x,Du)=\operatorname{div}F,} when 𝒜{\mathcal{A}} is a p-harmonic type ...
Clop Albert +2 more
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Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces
Advanced Nonlinear Studies, 2018 This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the ...
Yang Minghua, Fu Zunwei, Liu Suying
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Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces
Advances in Nonlinear Analysis, 2017 As an essential extension of the well known case β∈(12,1]{\beta\kern-1.0pt\in\kern-1.0pt({\frac{1}{2}},1]} to the hyper-dissipative case β∈(1,∞){\beta\kern-1.0pt\in\kern-1.0pt(1,\infty)}, this paper establishes both well-posedness and ill-posedness (not ...
Wang Yuzhao, Xiao Jie
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Some remarks on Riesz transforms on exterior Lipschitz domains
Forum of Mathematics, SigmaLet $n\ge 2$ and $\mathcal {L}=-\mathrm {div}(A\nabla \cdot )$ be an elliptic operator on $\mathbb {R}^n$ . Given an exterior Lipschitz domain $\Omega $ , let $\mathcal {L}_D$ be the elliptic operator $\mathcal {L}$
Renjin Jiang, Sibei Yang
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Some sharp bilinear space-time estimates for the wave equation [PDF]
Mathematika 62 (2016) 719-737, 2015 We prove a family of sharp bilinear space-time estimates for the half-wave propagator. As a consequence, for radially symmetric initial data, we establish sharp estimates of this kind for a range of exponents beyond the classical range.
arxiv +1 more source
Homothetic variant of fractional Sobolev space with application to Navier-Stokes system revisited [PDF]
arXiv, 2013 This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.
arxiv
Lectures on normal Coulomb frames in the normal bundle of twodimensional immersionen of higher codimension [PDF]
arXiv, 2009 We establish existence and regularity results for normal Coulomb frames in the normal bundle of two-dimensional surfaces of disc-type embedded in Euclidean spaces of higher dimensions.
arxiv
Global solutions for 2D quadratic Schrodinger equations [PDF]
arXiv, 2010 We prove global existence and scattering for a class of quadratic Schrodinger equations in dimension 2. The proof relies on the idea of space-time resonance.
arxiv