Estimates on fractional higher derivatives of weak solutions for the Navier-Stokes equations

We study weak solutions of the 3D Navier Stokes equations with L-2 initial data. We prove that del(alpha)u is locally integrable in space time for any real a such that 1 < alpha < 3. Up to now, only the second derivative del(alpha)u was known to be locally integrable by standard parabolic regularization. We also present sharp estimates of those quantities in weak-L-loc(4/(alpha+1)). These estimates depend only on the L-2-norm of the initial data and on the domain of integration. Moreover, they are valid even for alpha >= 3 as long as u is smooth. The proof uses a standard approximation of Navier Stokes from Leray and blow-up techniques. The local study is based on De Giorgi techniques with a new pressure decomposition. To handle the non-locality of fractional Laplacians, Hardy space and Maximal functions are introduced. (C) 2013 Elsevier Masson SAS. All rights reserved.open0

On global regularity of some bi-rotational Euler flows in R4\mathbb{R}^{4}

In this paper, we consider incompressible Euler flows in $\mathbb{R}^{4}$ under bi-rotational symmetry, namely solutions that are invariant under rotations in $\mathbb{R}^{4}$ fixing either the first two or last two axes. With the additional swirl-free assumption, our first main result gives local wellposedness of Yudovich-type solutions, extending the work of Danchin [Uspekhi Mat. Nauk 62(2007), no.3, 73-94] for axisymmetric flows in $\mathbb{R}^{3}$. The second main result establishes global wellposedness under additional decay conditions near the axes and at infinity. This in particular gives global regularity of $C^{\infty}$ smooth and decaying Euler flows in $\mathbb{R}^{4}$ subject to bi-rotational symmetry without swirl.Comment: 25 pages, 2 figure

On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations

In connection with the recent proposal for possible singularity formation at the boundary for solutions of 3d axi-symmetric incompressible Euler's equations (Luo and Hou, 2013), we study models for the dynamics at the boundary and show that they exhibit a finite-time blow-up from smooth data.Comment: A paragraph at the end of Section 2 and an appendix discussing kinetic energy conservation are adde

Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method

We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in L-2 for a class of large perturbations and for any bounded time interval. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. This is the first application of the relative entropy method developed by N. Leger [Arch. Ration. Mech. Anal., 199 (2011), pp. 761-778] and N. Leger and A. Vasseur [Arch. Ration. Mech. Anal., 201 (2011), pp. 271-302] to the study of an inviscid limit to a shock.open1

Genome-wide analysis of DNA methylation patterns in horse

Background: DNA methylation is an epigenetic regulatory mechanism that plays an essential role in mediating biological processes and determining phenotypic plasticity in organisms. Although the horse reference genome and whole transcriptome data are publically available the global DNA methylation data are yet to be known. Results: We report the first genome-wide DNA methylation characteristics data from skeletal muscle, heart, lung, and cerebrum tissues of thoroughbred (TH) and Jeju (JH) horses, an indigenous Korea breed, respectively by methyl-DNA immunoprecipitation sequencing. The analysis of the DNA methylation patterns indicated that the average methylation density was the lowest in the promoter region, while the density in the coding DNA sequence region was the highest. Among repeat elements, a relatively high density of methylation was observed in long interspersed nuclear elements compared to short interspersed nuclear elements or long terminal repeat elements. We also successfully identified differential methylated regions through a comparative analysis of corresponding tissues from TH and JH, indicating that the gene body regions showed a high methylation density. Conclusions: We provide report the first DNA methylation landscape and differentially methylated genomic regions (DMRs) of thoroughbred and Jeju horses, providing comprehensive DMRs maps of the DNA methylome. These data are invaluable resource to better understanding of epigenetics in the horse providing information for the further biological function analyses.open1

Genome-Wide Analysis of DNA Methylation before- and after Exercise in the Thoroughbred Horse with MeDIP-Seq

Athletic performance is an important criteria used for the selection of superior horses. However, little is known about exercise-related epigenetic processes in the horse. DNA methylation is a key mechanism for regulating gene expression in response to environmental changes. We carried out comparative genomic analysis of genome-wide DNA methylation profiles in the blood samples of two different thoroughbred horses before and after exercise by methylated-DNA immunoprecipitation sequencing (MeDIP-Seq). Differentially methylated regions (DMRs) in the pre- and post-exercise blood samples of superior and inferior horses were identified. Exercise altered the methylation patterns. After 30 min of exercise, 596 genes were hypomethylated and 715 genes were hypermethylated in the superior horse, whereas in the inferior horse, 868 genes were hypomethylated and 794 genes were hypermethylated. These genes were analyzed based on gene ontology (GO) annotations and the exercise-related pathway patterns in the two horses were compared. After exercise, gene regions related to cell division and adhesion were hypermethylated in the superior horse, whereas regions related to cell signaling and transport were hypermethylated in the inferior horse. Analysis of the distribution of methylated CpG islands confirmed the hypomethylation in the gene-body methylation regions after exercise. The methylation patterns of transposable elements also changed after exercise. Long interspersed nuclear elements (LINEs) showed abundance of DMRs. Collectively, our results serve as a basis to study exercise-based reprogramming of epigenetic traitsclose

The first whole genome and transcriptome of the cinereous vulture reveals adaptation in the gastric and immune defense systems and possible convergent evolution between the Old and New World vultures

Background: The cinereous vulture, Aegypius monachus, is the largest bird of prey and plays a key role in the ecosystem by removing carcasses, thus preventing the spread of diseases. Its feeding habits force it to cope with constant exposure to pathogens, making this species an interesting target for discovering functionally selected genetic variants. Furthermore, the presence of two independently evolved vulture groups, Old World and New World vultures, provides a natural experiment in which to investigate convergent evolution due to obligate scavenging. Results: We sequenced the genome of a cinereous vulture, and mapped it to the bald eagle reference genome, a close relative with a divergence time of 18 million years. By comparing the cinereous vulture to other avian genomes, we find positively selected genetic variations in this species associated with respiration, likely linked to their ability of immune defense responses and gastric acid secretion, consistent with their ability to digest carcasses. Comparisons between the Old World and New World vulture groups suggest convergent gene evolution. We assemble the cinereous vulture blood transcriptome from a second individual, and annotate genes. Finally, we infer the demographic history of the cinereous vulture which shows marked fluctuations in effective population size during the late Pleistocene. Conclusions: We present the first genome and transcriptome analyses of the cinereous vulture compared to other avian genomes and transcriptomes, revealing genetic signatures of dietary and environmental adaptations accompanied by possible convergent evolution between the Old World and New World vulturesopen