Almost sure existence of global weak solutions for super-critical Navier-Stokes equations

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which global energy bounds are proved. As a consequence, we obtain almost sure super-critical global weak solutions. We also show that in 2d these global weak solutions are unique.Comment: 22 pages, a revised argument in Section 5, the $d=3$ cas

Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

In this article, we consider a special class of initial data to the 3D Navier-Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier-Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm $B^{-1}_{\infty,\infty}$ that satisfies the conditions that we considered.Comment: 13 pages, updated references for v

Osmoregulation by means of a Hitherto unsuspected osmoregulatory organ in two grapsid crabs

Zoologica Africana 2 (1): 127-12

Specificity Between Lactobacilli And Hymenopteran Hosts Is The Exception Rather Than The Rule

Lactobacilli (Lactobacillales: Lactobacillaceae) are well known for their roles in food fermentation, as probiotics, and in human health, but they can also be dominant members of the microbiota of some species of Hymenoptera (ants, bees, and wasps). Honey bees and bumble bees associate with host-specific lactobacilli, and some evidence suggests that these lactobacilli are important for bee health. Social transmission helps maintain associations between these bees and their respective microbiota. To determine whether lactobacilli associated with social hymenopteran hosts are generally host specific, we gathered publicly available Lactobacillus 16S rRNA gene sequences, along with Lactobacillus sequences from 454 pyrosequencing surveys of six other hymenopteran species (three sweat bees and three ants). We determined the comparative secondary structural models of 16S rRNA, which allowed us to accurately align the entire 16S rRNA gene, including fast-evolving regions. BLAST searches and maximum-likelihood phylogenetic reconstructions confirmed that honey and bumble bees have host-specific Lactobacillus associates. Regardless of colony size or within-colony oral sharing of food (trophallaxis), sweat bees and ants associate with lactobacilli that are closely related to those found in vertebrate hosts or in diverse environments. Why honey and bumble bees associate with host-specific lactobacilli while other social Hymenoptera do not remains an open question. Lactobacilli are known to inhibit the growth of other microbes and can be beneficial whether they are coevolved with their host or are recruited by the host from environmental sources through mechanisms of partner choice.National Science Foundation PRFB-1003133, DEB-0919519Texas Higher Education Coordinating Board 01923, National Institutes of Health GM067317Integrative BiologyCellular and Molecular BiologyCenter for Computational Biology and BioinformaticsBrackenridge Field Laborator

Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index s=−1s=-1

This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\vec{u}_0,\theta_0)$ ($\nabla\cdot\vec{u}_0=0$) either in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\infty,\infty}}\times{B}^{-1,\epsilon}_{p,\infty}$ if $r\in[1,\infty]$, $\epsilon>0$ and $p\in(\frac{n}{2},\infty)$, where $B^{s,\epsilon}_{p,q}$ ($s\in\mathbb{R}$, $1\leq p,q\leq\infty$, $\epsilon>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s}_{p,q}$. We also prove that this system is well-posed for small initial data in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times({B}^{-1}_{\frac{n}{2},1}\cap{B^{-1,1}_{\frac{n}{2},\infty}})$.Comment: 18 page

On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in \cite{Chae1}.Comment: 16page

The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, i. e. \sup_{j\in\Z}\int_0^T\|\Delta_j(\na\times u)\|_\infty dt, where $\Delta_j$ is a frequency localization on $|\xi|\approx 2^j$.Comment: 12page

Fragmentation of the large subunit ribosomal RNA gene in oyster mitochondrial genomes

<p>Abstract</p> <p>Background</p> <p>Discontinuous genes have been observed in bacteria, archaea, and eukaryotic nuclei, mitochondria and chloroplasts. Gene discontinuity occurs in multiple forms: the two most frequent forms result from introns that are spliced out of the RNA and the resulting exons are spliced together to form a single transcript, and fragmented gene transcripts that are not covalently attached post-transcriptionally. Within the past few years, fragmented ribosomal RNA (rRNA) genes have been discovered in bilateral metazoan mitochondria, all within a group of related oysters.</p> <p>Results</p> <p>In this study, we have characterized this fragmentation with comparative analysis and experimentation. We present secondary structures, modeled using comparative sequence analysis of the discontinuous mitochondrial large subunit rRNA genes of the cupped oysters <it>C. virginica, C. gigas</it>, and <it>C. hongkongensis</it>. Comparative structure models for the large subunit rRNA in each of the three oyster species are generally similar to those for other bilateral metazoans. We also used RT-PCR and analyzed ESTs to determine if the two fragmented LSU rRNAs are spliced together. The two segments are transcribed separately, and not spliced together although they still form functional rRNAs and ribosomes.</p> <p>Conclusions</p> <p>Although many examples of discontinuous ribosomal genes have been documented in bacteria and archaea, as well as the nuclei, chloroplasts, and mitochondria of eukaryotes, oysters are some of the first characterized examples of fragmented bilateral animal mitochondrial rRNA genes. The secondary structures of the oyster LSU rRNA fragments have been predicted on the basis of previous comparative metazoan mitochondrial LSU rRNA structure models.</p

Ichthyophonus irregularis sp. nov. from the yellowtail flounder Limanda ferruginea from the Nova Scotia shelf

A previously described unusual form of the protistan parasite Ichthyophonus, differing in morphological and developmental features from I. hoferi sensu Plehn & Mulsow, was recovered from yellowtail flounder Limanda ferruginea Storer from the Brown's Bank area of the Nova Scotia shelf. The nuclear gene encoding the rRNA of the small ribosomal subunit was amplified from this unusual form of Ichthyophonus using the polymerase chain reaction, sequenced and aligned with other eukaryote small subunit (ssu)-rDNAs. Inferred phylogenetic trees clearly show that its ssu-rDNA is distinct from those of 2 isolates of I. hoferi sensu Plehn & Mulsow from different hosts and geographical locations (herring in the North Sea, and yellowtail flounder from the Nova Scotia shelf). We consider the unusual form to be a separate species, I. irregularis. The occurrence of a second, distinct type of Ichthyophonus within a single host species raises the possibility that ichthyophoniasis could be produced by different (although related) pathogens, and in some cases, by concurrent infections of the two

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy