Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations

We consider the incompressible Euler equations on ${\mathbb R}^d$, where $d \in \{ 2,3 \}$. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey-class radius). (b) In Lagrangian coordinates the equations are well-posed in highly anisotropic spaces, e.g.~Gevrey-class regularity in the label $a_1$ and Sobolev regularity in the labels $a_2,...,a_d$. (c) In Eulerian coordinates both results (a) and (b) above are false.Comment: 22 page

On the inviscid limit of the Navier-Stokes equations

We consider the convergence in the $L^2$ norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no back-flow in the trace of the Euler flow, and of a lower bound for the Navier-Stokes vorticity is assumed in a Kato-like boundary layer, then the inviscid limit holds.Comment: Improved the main result and fixed a number of typo

Psychological Barriers in Long Term Non-Operative Treatment of Retroperitoneal Hematoma

The retroperitoneal hematoma can have, mainly, a traumatic etiology - blunt abdominal trauma (falls from height, road accidents, aggression of any kind, etc.), or open (incised wounds, puncture, penetration or gunshot wounds). Ruptured arterial aneurysms can cause hemorrhage in the retroperitoneal space. There is also spontaneous retroperitoneal trauma in patients with chronic treatment with anticoagulant or antiaggregant drugs (1). Hemorrhage in the retroperitoneal space can be iatrogenic, after surgical, open or laparoscopic, interventions (2, 3). A particular type of retroperitoneal hematoma is the psoas muscle hematoma in patients with chronic oral anticoagulant treatment (Acenocumarol, Warfarin)

Perforated small intestine in a patient with T-cell lymphoma; a rare cause of peritonitis

The nontraumatic perforations of the small intestine are pathological entities with particular aspects in respect to diagnosis and treatment. These peculiarities derive from the nonspecific clinical expression of the peritonitis syndrome, and from the multitude of causes that might be the primary sources of the perforation: foreign bodies, inflammatory diseases, tumors, infectious diseases, etc. Accordingly, in most cases intestinal perforation is discovered only by laparotomy and the definitive diagnosis is available only after histopathologic examination. Small bowel malignancies are rare; among them, lymphomas rank third in frequency, being mostly B-cell non Hodgkin lymphomas. Only 10% of non-Hodgkin lymphomas are with T-cell. We report the case of a 57 years’ old woman with intestinal T-cell lymphoma, whose first clinical symptomatology was related to a complication represented by perforation of the small intestine. Laparotomy performed in emergency identified an ulcerative lesion with perforation in the jejunum, which required segmental enterectomy with anastomosis. The nonspecific clinical manifestations of intestinal lymphomas make from diagnosis a difficult procedure. Due to the fact that surgery does not have a definite place in the treatment of the small intestinal lymphomas (for cases complicated with perforation), and beyond the morbidity associated with the surgery performed in emergency conditions, prognosis of these patients is finally given by the possibility to control the systemic disease through adjuvant therapy

Therapeutic approach for Amyand’s hernia; a case report

In very few cases stated in the literature, the vermiform appendix might be contained in a hernial sac. This distinctive pathology is described as Amyand\u27s hernia and has the very small occurrence of about 1%. We report the case of a 62-year-old man that presented for a reducible tumoral mass located in the right inguinal region. Amyand’s hernia was the intraoperative diagnostic. We performed hernioplasty (using the Lichtenstein tension-free mesh repair with a composite polypropylene mesh) without appendectomy. This case matches the type 1 Lossanoff and Basson’s classification and has no facile management. Due to the clinical specificities of each case that presents with defining features of an Amyand’s hernia, surgical management depends on the recommendations stated in the literature, as well as the surgeon’s judgment based on experience