We study the nonhomogeneous boundary value problem for the Navier-Stokes equations of steady motion of a viscous incompressible fluid in arbitrary bounded multiply connected plane or axiallysymmetric spatial domains. We prove that this problem has a solution under the sole necessary condition of zero total flux through the boundary. The problem was formulated by Jean Leray 80 years ago. The proof of the main result uses Bernoulli's law for a weak solution to the Euler equations.

We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a two-dimensional bounded multiply connected domain Ω = Ω 1 \ Ω 2 , Ω 2 ⊂ Ω 1 . We prove that this problem has a solution if the flux F of the boundary datum through ∂Ω 2 is nonnegative (

Our findings, in agreement with previous literature, encourage further studies for a better comprehension of the therapeutic potential of TRPM8 blockers as novel agents for pain management.

We study a nonhomogeneous boundary-value problem for the steady-state Navier-Stokes equations in a two-dimensional exterior domain with two orthogonal symmetry axes. The existence of a solution which tends to zero uniformly at infinity is proved under suitable parity conditions on the data of the problem. The result is obtained for arbitrary values of the flux of the boundary datum.

Chemotherapy-induced peripheral neuropathy (CIPN) is a type of neuropathic pain that represents a frequent and serious consequence of chemotherapy agents. Over the last years, significant progress has been achieved in elucidating the underlying pathogenesis of CIPN. The interference of taxanes with microtubule has been proposed as a mechanism that leads to altered axonal transport and to permanent neurological damages. The inflammatory process activated by chemotherapeutic agents has been considered as a potential trigger of nociceptive process in CIPN.In this study we investigated the effect of reparixin, an inhibitor of CXCR1/CXCR2, in suppressing the development of paclitaxel-induced nociception in rats. Moreover, reparixin activity in reversing the neurotoxic effects induced by paclitaxel or GRO/KC in F11 cells was also analyzed.Reparixin administered by continuous infusion ameliorated paclitaxel-induced mechanical and cold allodynia in rats. In F11 cells, reparixin was able to inhibit the increase of acetyladed α-tubulin induced both by paclitaxel and GRO/KC. The subsequent experiments were performed in order to dissect the signal transduction pathways under GRO/KC control, eventually modulated by paclitaxel and/or reparixin. To this aim we found that reparixin significantly counteracted p-FAK, p-JAK2/p-STAT3, and PI3K-p-cortactin activation induced either by paclitaxel or GRO/KC.Overall the present results have identified IL-8/CXCR1/2 pathway as a mechanism involved in paclitaxel-induced peripheral neuropathy. In particular, the obtained data suggest that the inhibition of CXCR1/2 combined with standard taxane therapy, in addition to potentiating the taxane anti-tumor activity can reduce chemotherapy-induced neurotoxicity, thus giving some insight for the development of novel treatments.