Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Weak-strong uniqueness for the isentropic compressible Navier-Stokes system

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.Comment: 12 page

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

Transmission Problems for the Navier–Stokes and Darcy–Forchheimer–Brinkman Systems in Lipschitz Domains on Compact Riemannian Manifolds

M. Kohr acknowledges the support of the Grant PN-II-ID-PCE-2011-3-0994 of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI. The research has been also partially supported by the Grant EP/M013545/1: “Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs” from the EPSRC, UK

Compressible Navier–Stokes system with hard sphere pressure law and general inflow–outflow boundary conditions

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Comparison of the chemical composition, textural characteristics, and sensory properties of North and South Korean native chickens and commercial broilers

The objective of this study was to compare the quality characteristics of chicken breast and thigh meat from North Korean native chickens (NKNC), South Korean native chickens (SKNC, woorimotdak), and commercial broilers (CB). NKNC thigh meat had a higher crude protein content than CB. In addition, the breasts of NKNC and CB had higher pH values than that of SKNC, but the cooking loss was higher in NKNC. The surface color of the breast and thigh meat of NKNC was darker and redder than that of SKNC and CB. The total collagen content of the breast and thigh muscles was the highest in NKNC, followed by SKNC and CB. A similar trend occurred with breast meat hardness. The content of arachidonic and docosahexaenoic acids was higher in both the breast and thigh muscles of NKNC than in those of the other groups, while the concentrations of linoleic and linolenic acids were higher only in thigh meat. Sensory evaluation did not show any differences among the three different strains of chicken except for the meat color. Sensory panelists preferred thigh meat from SKNC and CB to that of NKNC due to the strong dark color of the NKNC. Based on these results, NKNC had harder breasts based on texture, as well as a darker surface color and higher composition of long chain polyunsaturated fatty acids than CB. The quality characteristics of SKNC tested in this study were intermediate between NKNC and CB; however, SKNC may have a better chance of acceptance by Korean consumers due to the undesirable color of NKNC.Hee-Joon Jeon, Jun-Ho Choe, Yeonkook Jung, Zbigniew A. Kruk, Dong-Gyun Lim, and Cheorun J