Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals

We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in $\mathbb R^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we first prove the existence of a global weak solution in $\mathbb R^3$. The large-time behavior of a global weak solution is also established.Comment: arXiv admin note: text overlap with arXiv:1110.0053, arXiv:1004.4749 by other author

Chemicals having estrogenic activity can be released from some bisphenol a-free, hard and clear, thermoplastic resins

Background: Chemicals that have estrogenic activity (EA) can potentially cause adverse health effects in mammals including humans, sometimes at low doses in fetal through juvenile stages with effects detected in adults. Polycarbonate (PC) thermoplastic resins made from bisphenol A (BPA), a chemical that has EA, are now often avoided in products used by babies. Other BPA-free thermoplastic resins, some hypothesized or advertised to be EA-free, are replacing PC resins used to make reusable hard and clear thermoplastic products such as baby bottles. Methods: We used two very sensitive and accurate in vitro assays (MCF-7 and BG1Luc human cell lines) to quantify the EA of chemicals leached into ethanol or water/saline extracts of fourteen unstressed or stressed (autoclaving, microwaving, UV radiation) thermoplastic resins. Estrogen receptor (ER)-dependent agonist responses were confirmed by their inhibition with the ER antagonist ICI 182,780. Results: Our data showed that some (4/14) unstressed and stressed BPA-free thermoplastic resins leached chemicals having significant levels of EA, including one polystyrene (PS), and three Tritan™ resins, the latter reportedly EA-free. Exposure to UV radiation in natural sunlight resulted in an increased release of EA from Tritan™ resins. Triphenyl-phosphate (TPP), an additive used to manufacture some thermoplastic resins such as Tritan™, exhibited EA in both MCF-7 and BG1Luc assays. Ten unstressed or stressed glycol-modified polyethylene terephthalate (PETG), cyclic olefin polymer (COP) or copolymer (COC) thermoplastic resins did not release chemicals with detectable EA under any test condition. Conclusions: This hazard survey study assessed the release of chemicals exhibiting EA as detected by two sensitive, widely used and accepted, human cell line in vitro assays. Four PC replacement resins (Tritan™ and PS) released chemicals having EA. However, ten other PC-replacement resins did not leach chemicals having EA (EA-free-resins). These results indicate that PC-replacement plastic products could be made from EA-free resins (if appropriate EA-free additives are chosen) that maintain advantages of re-usable plastic items (price, weight, shatter resistance) without releasing chemicals having EA that potentially produce adverse health effects on current or future generations.This work was supported by the following NIH/NIEHS grants: R44 ES011469, 01–03 (CZY); 1R43/44 ES014806, 01–03 (CZY); subcontract (CZY, PI) on an NIH Grant 01–03 43/44ES018083-01. This work was also supported by NIH grants to MSD (P42 ES004699), and DJK and SIY (1R43ES018083-01-03, NIEHS 1R44ES019442-01-03 and NIEHS 2R44ES016964-01-03).Neuroscienc

Global Stability and Non-Vanishing Vacuum States of 3D Compressible Navier-Stokes Equations

We investigate the global stability and non-vanishing vacuum states of large solutions to the compressible Navier-Stokes equations on the torus $\mathbb{T}^3$, and the main novelty of this work is three-fold: First, under the assumption that the density $\rho({\bf{x}}, t)$ verifies $\sup_{t\geq 0}\|\rho(t)\|_{L^\infty}\leq M$, it is shown that the solutions converge to equilibrium state exponentially in $L^2$-norm. Second, by employing some new thoughts, we also show that the density converges to its equilibrium state exponentially in $L^\infty$-norm if additionally the initial density $\rho_0({\bf{x}})$ satisfies $\inf_{{\bf{x}}\in\mathbb{T}^3}\rho_0({\bf{x}})\geq c_0>0$. Finally, we prove that the vacuum states will not vanish for any time provided that the vacuum states are present initially. This phenomenon is totally new and somewhat surprising, and particularly is in contrast to the previous work of [H. L. Li et al., Commun. Math. Phys., 281 (2008), 401-444], where the authors showed that the vacuum states must vanish within finite time for the 1D compressible Navier-Stokes equations with density-dependent viscosity $\mu(\rho)=\rho^\alpha$ with $\alpha>1/2$.Comment: 17 page

Divergent Annexin A1 expression in periphery and gut is associated with systemic immune activation and impaired gut immune response during SIV infection.

HIV-1 disease progression is paradoxically characterized by systemic chronic immune activation and gut mucosal immune dysfunction, which is not fully defined. Annexin A1 (ANXA1), an inflammation modulator, is a potential link between systemic inflammation and gut immune dysfunction during the simian immunodeficiency virus (SIV) infection. Gene expression of ANXA1 and cytokines were assessed in therapy-naïve rhesus macaques during early and chronic stages of SIV infection and compared with SIV-negative controls. ANXA1 expression was suppressed in the gut but systemically increased during early infection. Conversely, ANXA1 expression increased in both compartments during chronic infection. ANXA1 expression in peripheral blood was positively correlated with HLA-DR+CD4+ and CD8+ T-cell frequencies, and negatively associated with the expression of pro-inflammatory cytokines and CCR5. In contrast, the gut mucosa presented an anergic cytokine profile in relation to ANXA1 expression. In vitro stimulations with ANXA1 peptide resulted in decreased inflammatory response in PBMC but increased activation of gut lymphocytes. Our findings suggest that ANXA1 signaling is dysfunctional in SIV infection, and may contribute to chronic inflammation in periphery and with immune dysfunction in the gut mucosa. Thus, ANXA1 signaling may be a novel therapeutic target for the resolution of immune dysfunction in HIV infection

On instability of a generic compressible two-fluid model in R3\mathbb R^3

We are concerned with the instability of a generic compressible two-fluid model in the whole space $\mathbb{R}^3$, where the capillary pressure $f(\alpha^-\rho^-)=P^+-P^-\neq 0$ is taken into account. For the case that the capillary pressure is a strictly decreasing function near the equilibrium, namely, $f'(1)<0$, Evje-Wang-Wen established global stability of the constant equilibrium state for the three-dimensional Cauchy problem under some smallness assumptions. Recently, Wu-Yao-Zhang proved global stability of the constant equilibrium state for the case $P^+=P^-$ (corresponding to $f'(1)=0$). In this work, we investigate the instability of the constant equilibrium state for the case that the capillary pressure is a strictly increasing function near the equilibrium, namely, $f'(1)>0$. First, by employing Hodge decomposition technique and making detailed analysis of the Green's function for the corresponding linearized system, we construct solutions of the linearized problem that grow exponentially in time in the Sobolev space $H^k$, thus leading to a global instability result for the linearized problem. Moreover, with the help of the global linear instability result and a local existence theorem of classical solutions to the original nonlinear system, we can then show the instability of the nonlinear problem in the sense of Hadamard by making a delicate analysis on the properties of the semigroup. Therefore, our result shows that for the case $f'(1)>0$, the constant equilibrium state of the two-fluid model is linearly globally unstable and nonlinearly locally unstable in the sense of Hadamard, which is in contrast to the cases $f'(1)<0$ and $P^+=P^-$ (corresponding to $f'(1)=0$) where the constant equilibrium state of the two--fluid model is nonlinearly globally stable.Comment: 17. arXiv admin note: substantial text overlap with arXiv:2204.10706, arXiv:2108.06974, arXiv:2010.1150