New entropy for Korteweg's system, existence of global weak solution and Prodi-Serrin theorem

This work is devoted to prove new entropy estimates for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see \cite{fDS}), which can be used as a phase transition model. More precisely we will derive new estimates for the density and we will give a new structure for the Korteweg system which allow us to obtain the existence of global weak solution. The key of the proof comes from the introduction of a new effective velocity.The proof is widely inspired from the works of A. Mellet and A. Vasseur (see \cite{fMV}). In a second part, we shall give a Prody-Serrin blow-up criterion for this system which widely improves the results of \cite{Hprepa} and the known results on compressible systems

Well-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N≥2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves the analysis of R. Danchin (2007) in [13], of Q. Chen et al. (2010) in [8] and of B. Haspot (2009, 2010) in [15,16] inasmuch as we may take initial density in Bp,1Np with 1≤p<+∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one the coupling between the density and the velocity. In particular for the first time we obtain uniqueness without imposing hypothesis on the gradient of the density

Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves the analysis of Danchin and of the author inasmuch as we may take initial density in B N/p p,1 with 1 ≤ p &lt; +∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one of the couplings between the density and the velocity. In particular, our result is the first in which we obtain uniqueness without imposing hypothesis on the gradient of the density

Existence of global strong solutions in critical spaces for barotropic viscous fluids

This paper is dedicated to the study of viscous compressible barotropic fluids in dimension $N\geq2$. We address the question of the global existence of strong solutions for initial data close from a constant state having critical Besov regularity. In a first time, this article show the recent results of \cite{CD} and \cite{CMZ} with a new proof. Our result relies on a new a priori estimate for the velocity, where we introduce a new structure to \textit{kill} the coupling between the density and the velocity as in \cite{H2}. We study so a new variable that we call effective velocity. In a second time we improve the results of \cite{CD} and \cite{CMZ} by adding some regularity on the initial data in particular $\rho_{0}$ is in $H^{1}$. In this case we obtain global strong solutions for a class of large initial data on the density and the velocity which in particular improve the results of D. Hoff in \cite{5H4}. We conclude by generalizing these results for general viscosity coefficients

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

The sharp-interface limit for the Navier--Stokes--Korteweg equations

We investigate the sharp-interface limit for the Navier--Stokes--Korteweg model, which is an extension of the compressible Navier--Stokes equations. By means of compactness arguments, we show that solutions of the Navier--Stokes--Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions

Nonlinear Instability for Nonhomogeneous Incompressible Viscous Fluids

We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor steady-state solution with heavier density with increasing height (referred to the Rayleigh-Taylor instability). We first analyze the equations obtained from linearization around the steady density profile solution. Then we construct solutions of the linearized problem that grow in time in the Sobolev space Hk, thus leading to a global instability result for the linearized problem. With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations, we can then demonstrate the instability of the nonlinear problem in some sense. Our analysis shows that the third component of the velocity already induces the instability, this is different from the previous known results.Comment: 24 page

Human Cytomegalovirus Entry into Dendritic Cells Occurs via a Macropinocytosis-Like Pathway in a pH-Independent and Cholesterol-Dependent Manner

Human cytomegalovirus (HCMV) is a ubiquitous herpesvirus that is able to infect fibroblastic, epithelial, endothelial and hematopoietic cells. Over the past ten years, several groups have provided direct evidence that dendritic cells (DCs) fully support the HCMV lytic cycle. We previously demonstrated that the C-type lectin dendritic cell-specific intercellular adhesion molecule-3-grabbing non-integrin (DC-SIGN) has a prominent role in the docking of HCMV on monocyte-derived DCs (MDDCs). The DC-SIGN/HCMV interaction was demonstrated to be a crucial and early event that substantially enhanced infection in trans, i.e., from one CMV-bearing cell to another non-infected cell (or trans-infection), and rendered susceptible cells fully permissive to HCMV infection. Nevertheless, nothing is yet known about how HCMV enters MDDCs. In this study, we demonstrated that VHL/E HCMV virions (an endothelio/dendrotropic strain) are first internalized into MDDCs by a macropinocytosis-like process in an actin- and cholesterol-dependent, but pH-independent, manner. We observed the accumulation of virions in large uncoated vesicles with endosomal features, and the virions remained as intact particles that retained infectious potential for several hours. This trans-infection property was specific to MDDCs because monocyte-derived macrophages or monocytes from the same donor were unable to allow the accumulation of and the subsequent transmission of the virus. Together, these data allowed us to delineate the early mechanisms of the internalization and entry of an endothelio/dendrotropic HCMV strain into human MDDCs and to propose that DCs can serve as a "Trojan horse" to convey CMV from entry sites to other locations that may favor the occurrence of either latency or acute infection