Strichartz estimates for the water-wave problem with surface tension

Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales depending on the size of the frequencies. We infer that a solution $u$ of the dispersive equation we introduce satisfies local-in-time Strichartz estimates with loss in derivative: $$\| u \|_{L^p([0,T]) W^{s-1/p,q}(\mathbb{R})} \leq C, \qquad \frac{2}{p} + \frac{1}{q} = {1/2},$$ where $C$ depends on $T$ and on the norms of the initial data in $H^s \times H^{s-3/2}$. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.Comment: Fixed typos and mistakes. Merged with arXiv:0809.451

Behavioral assessment of neuropathic pain, fatigue, and anxiety in experimental autoimmune encephalomyelitis (EAE) and attenuation by interleukin-10 gene therapy

Relapsing-remitting multiple sclerosis is commonly associated with motor impairments, neuropathic pain, fatigue, mood disorders, and decreased life expectancy. However, preclinical pharmacological studies predominantly rely on clinical scoring of motor deficit as the sole behavioral endpoint. Thus, the translational potential of these studies is limited. Here, we have assessed the therapeutic potential of a novel anti-inflammatory interleukin-10 (IL-10) non-viral gene therapy formulation (XT-101-R) in a rat relapsing remitting experimental autoimmune encephalomyelitis (EAE) model. EAE induced motor deficits and neuropathic pain as reflected by induction of low-threshold mechanical allodynia, suppressed voluntary wheel running, decreased social exploration, and was associated with markedly enhanced mortality. We also noted that voluntary wheel running was depressed prior to the onset of motor deficit, and may therefore serve as a predictor of clinical symptoms onset. XT-101-R was intrathecally dosed only once at the onset of motor deficits, and attenuated each of the EAE-induced symptoms and improved survival, relative to vehicle control. This is the first pharmacological assessment of such a broad range of EAE symptoms, and provides support for IL-10 gene therapy as a clinical strategy for the treatment of multiple sclerosis.Peter M.Grace, Lisa C.Loram, John P.Christianson, Keith A.Strand, Johanna G.Flyer-Adams, Kathryn R.Penzkover ... et al