Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations

In this paper, we consider a global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations (\textit{ANS}). In order to do so, we first introduce the scaling invariant Besov-Sobolev type spaces, $B^{-1+\frac{2}{p},{1/2}}_{p}$ and $B^{-1+\frac{2}{p},{1/2}}_{p}(T)$, $p\geq2$. Then, we prove the global wellposedness for (\textit{ANS}) provided the initial data are sufficient small compared to the horizontal viscosity in some suitable sense, which is stronger than $B^{-1+\frac{2}{p},{1/2}}_{p}$ norm. In particular, our results imply the global wellposedness of (\textit{ANS}) with high oscillatory initial data.Comment: 39 page

Large time behavior for vortex evolution in the half-plane

In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states for half-plane vortex dynamics decompose naturally into a nonlinear superposition of soliton-like states. Our approach is to combine techniques developed in the study of vortex confinement with weak convergence tools in order to study the asymptotic behavior of a self-similar rescaling of a solution of the incompressible 2D Euler equations on a half plane with compactly supported, nonnegative initial vorticity.Comment: 30 pages, no figure

Magnetic Fourier Integral Operators

In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral Operators Theory to the case with a magnetic field, proving composition theorems, continuity theorems in 'magnetic' Sobolev spaces and Egorov type theorems. The main application is the representation of the evolution group generated by a 1-st order 'magnetic' pseudodifferential operator (in particular the relativistic Schr\"{o}dinger operator with magnetic field) as such a 'magnetic' Fourier Integral Operator. As a consequence of this representation we obtain some estimations for the distribution kernel of this evolution group and a result on the propagation of singularities

Idiopathic normal pressure hydrocephalus: A brief review

Idiopathic normal pressure hydrocephalus (INPH) is a neurodegenerative disease which affects the elderly, with a significant prevalence in the general population (0,2% - 5,9%), thus a common pathology encountered by neurologists and neurosurgeons, alike. Although the widespread availability of modern imaging techniques has facilitated the diagnosis of this disorder, the clinical manifestations can often be misleading. Also, an overlap with other degenerative or psychiatric diseases can make the differential diagnosis even more challenging. Cerebrospinal fluid (CSF) diversion procedures are the first line of treatment for INPH. Nowadays, there are several shunting options available, including: ventriculoperitoneal (the most commonly used), ventriculoatrial, ventriculopleural, ventriculosternal, lumboperitoneal, endoscopic third ventriculostomy. Choosing a procedure tailored to the individual patient is essential for therapeutic success. Although they are generally straightforward surgical interventions, they associate a high rate of failure, regardless of procedure used, which emphasizes the need for regular clinical and imagistic follow-up. Thus, INPH remains a disease where there is significant room for improvement, both in diagnosis and treatment

Do acute ischemic stroke patients receive the right treatment in non-stroke units?

Background: Modern treatment of acute ischemic stroke includes thrombolysis and thrombectomy performed for eligible patients in specialized stroke centers. However, a number of patients are admitted in Neurosurgical or Intensive Care Departments of emergency hospitals, units where routine treatment strategies are applied.Objective: To evaluate the management of patients admitted in these departments that do not benefit from thrombolytic or endovascular treatment.Methods: A retrospective analysis was performed, including all patients admitted to the Neurosurgery Department and Intensive Care Unit (ICU) of the “St. Pantelimon” Clinical Emergency Hospital with the primary diagnosis of acute ischemic stroke in the year 2016. The following data was retrospectively collected: patient age and sex, comorbidities, risk factors for ischemic stroke, level of consciousness at admission, neurological deficits, stroke location, blood glucose levels, interval from stroke onset to admission, treatment and discharge status.Results: In 2016, 63 patients with primary diagnosis of acute ischemic stroke confirmed by head CT scan were admitted in our hospital. None presented indication for decompressive craniectomy. Over a half of them (57,14%) were comatose. The majority of patients admitted to the ICU (76,47%) received glucose 10% infusions in the first 24 hours from admission, despite increased blood glucose levels at admission. A number of 38 (60,32%) of these patients died.Conclusions: Patients with acute ischemic stroke should be treated in stroke units with proper equipment and specialists. National public health institutions should take the necessary measures in order to ensure that patients get to the best facility in order to receive the right therapy in the right amount of time