Blow-up of critical Besov norms at a potential Navier-Stokes singularity

We show that the spatial norm of any strong Navier-Stokes solution in the space X must become unbounded near a singularity, where X may be any critical homogeneous Besov space in which local existence of strong solutions to the 3-d Navier-Stokes system is known. In particular, the regularity of these spaces can be arbitrarily close to -1, which is the lowest regularity of any Navier-Stokes critical space. This extends a well-known result of Escauriaza-Seregin-Sverak (2003) concerning the Lebesgue space $L^3$, a critical space with regularity 0 which is continuously embedded into the spaces we consider. We follow the "critical element" reductio ad absurdum method of Kenig-Merle based on profile decompositions, but due to the low regularity of the spaces considered we rely on an iterative algorithm to improve low-regularity bounds on solutions to bounds on a part of the solution in spaces with positive regularity

High-yield nontoxic gene transfer through conjugation of the CM\u2081\u2088-Tat\u2081\u2081 chimeric peptide with nanosecond electric pulses

We report a novel nontoxic, high-yield, gene delivery system based on the synergistic use of nanosecond electric pulses (NPs) and nanomolar doses of the recently introduced CM18-Tat11 chimeric peptide (sequence of KWKLFKKIGAVLKVLTTGYGRKKRRQRRR, residues 1-7 of cecropin-A, 2-12 of melittin, and 47-57 of HIV-1 Tat protein). This combined use makes it possible to drastically reduce the required CM18-Tat11 concentration and confines stable nanopore formation to vesicle membranes followed by DNA release, while no detectable perturbation of the plasma membrane is observed. Two different experimental assays are exploited to quantitatively evaluate the details of NPs and CM18-Tat11 cooperation: (i) cytofluorimetric analysis of the integrity of synthetic 1,2-dioleoyl-sn-glycero-3-phosphocholine giant unilamellar vesicles exposed to CM18-Tat11 and NPs and (ii) the in vitro transfection efficiency of a green fluorescent protein-encoding plasmid conjugated to CM18-Tat11 in the presence of NPs. Data support a model in which NPs induce membrane perturbation in the form of transient pores on all cellular membranes, while the peptide stabilizes membrane defects selectively within endosomes. Interestingly, atomistic molecular dynamics simulations show that the latter activity can be specifically attributed to the CM18 module, while Tat11 remains essential for cargo binding and vector subcellular localization. We argue that this result represents a paradigmatic example that can open the way to other targeted delivery protocols

Large Time Behavior of the Navier-Stokes Flow

International audienceDifferent results related to the asymptotic behavior of incompressible fluid equations are analyzed as time tends to infinity. The main focus is on the solutions to the Navier-Stokes equations, but in the final section a brief discussion is added on solutions to Magneto-Hydrodynamics, Liquid crystals, Quasi-Geostrophic and Boussinesq equations. Consideration is given to results on decay, asymptotic profiles, and stability for finite and nonfinite energy solutions

Mortality reduction by post-dilution online-haemodiafiltration : A cause-specific analysis

Background. From an individual participant data (IPD) meta-analysis from four randomized controlled trials comparing haemodialysis (HD) with post-dilution online-haemodiafiltration (ol-HDF), previously it appeared that HDF decreases all-cause mortality by 14% (95% confidence interval 25; 1) and fatal cardiovascular disease (CVD) by 23% (39; 3). Significant differences were not found for fatal infections and sudden death. So far, it is unclear, however, whether the reduced mortality risk of HDF is only due to a decrease in CVD events and if so, which CVD in particular is prevented, if compared with HD. Methods. The IPD base was used for the present study. Hazard ratios and 95% confidence intervals for cause-specific mortality overall and in thirds of the convection volume were calculated using the Cox proportional hazard regression models. Annualized mortality and numbers needed to treat (NNT) were calculated as well. Results. Besides 554 patients dying from CVD, fatal infections and sudden death, 215 participants died from 'other causes', such as withdrawal from treatment and malignancies. In this group, the mortality risk was comparable between HD and ol-HDF patients, both overall and in thirds of the convection volume. Subdivision of CVD mortality in fatal cardiac, non-cardiac and unclassified CVD showed that ol-HDF was only associated with a lower risk of cardiac casualties [0.64 (0.61; 0.90)]. Annual mortality rates also suggest that the reduction in CVD death is mainly due to a decrease in cardiac fatalities, including both ischaemic heart disease and congestion. Overall, 32 and 75 patients, respectively, need to be treated by high-volume HDF (HV-HDF) to prevent one all-cause and one CVD death, respectively, per year. Conclusion. The beneficial effect of ol-HDF on all-cause and CVD mortality appears to be mainly due to a reduction in fatal cardiac events, including ischaemic heart disease as well as congestion. In HV-HDF, the NNT to prevent one CVD death is 75 per year

Mortality reduction by post-dilution online-haemodiafiltration : A cause-specific analysis

Background. From an individual participant data (IPD) meta-analysis from four randomized controlled trials comparing haemodialysis (HD) with post-dilution online-haemodiafiltration (ol-HDF), previously it appeared that HDF decreases all-cause mortality by 14% (95% confidence interval 25; 1) and fatal cardiovascular disease (CVD) by 23% (39; 3). Significant differences were not found for fatal infections and sudden death. So far, it is unclear, however, whether the reduced mortality risk of HDF is only due to a decrease in CVD events and if so, which CVD in particular is prevented, if compared with HD. Methods. The IPD base was used for the present study. Hazard ratios and 95% confidence intervals for cause-specific mortality overall and in thirds of the convection volume were calculated using the Cox proportional hazard regression models. Annualized mortality and numbers needed to treat (NNT) were calculated as well. Results. Besides 554 patients dying from CVD, fatal infections and sudden death, 215 participants died from 'other causes', such as withdrawal from treatment and malignancies. In this group, the mortality risk was comparable between HD and ol-HDF patients, both overall and in thirds of the convection volume. Subdivision of CVD mortality in fatal cardiac, non-cardiac and unclassified CVD showed that ol-HDF was only associated with a lower risk of cardiac casualties [0.64 (0.61; 0.90)]. Annual mortality rates also suggest that the reduction in CVD death is mainly due to a decrease in cardiac fatalities, including both ischaemic heart disease and congestion. Overall, 32 and 75 patients, respectively, need to be treated by high-volume HDF (HV-HDF) to prevent one all-cause and one CVD death, respectively, per year. Conclusion. The beneficial effect of ol-HDF on all-cause and CVD mortality appears to be mainly due to a reduction in fatal cardiac events, including ischaemic heart disease as well as congestion. In HV-HDF, the NNT to prevent one CVD death is 75 per year