Entire solutions of hydrodynamical equations with exponential dissipation

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at high wavenumbers $|k|$. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any $C<1/(2\ln 2)$. The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with $C= C_\star =1/\ln2$. The same behavior with a universal constant $C_\star$ is conjectured for the Navier--Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier--Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres

T2015 Multivariate Analysis of Predictors for Severity of Mucosal Lesions in Patients with GERD Symptoms (Mapsomal): A Clinical, Epidemiological and Endoscopic Survey

Background: Improvement of symptoms plays a critical role for assessment of treatment outcome in patients with gastroesophageal reflux disease (GERD). Interestingly, most data on long-term outcome of these patients come from clinical trials that assessed the response to treatment in highly standardized trial conditions, with very strict entry criteria and frequent follow-up visits, that are unlikely to be representative of outcomes in standard clinical settings. AIM: To assess the long-term outcome of patients presenting with GERD symptoms for diagnostic work-up in a usual clinical care setting and the clinical predictors of response/ non-response. This abstract summarizes the interim analysis after recruitment of 100 patients. Methods: One hundred patients referred for endoscopic assessment of suspected GERD within a single metropolitan area health service were recruited; 82 consecutive patients from the Royal Adelaide Hospital (RAH) and 28 from the Lyell McEwen Health Centre (LMH). Symptoms and psychological co-morbidities were assessed utilizing the Bowel Disease Ques- tionnaire, the Hospital Anxiety and Depression Scale and the Nepean Dyspepsia Index. Questionnaires were mailed to the patients. Data on endoscopic findings at referral using the Los Angeles (LA) classification were included. As this was an observational study, routine clinical management by the referring GP was not altered. RESULTS: 68 patients were on proton pump inhibitor (PPI) therapy while 31 patients did not receive the treatment. In 58 patients endoscopy revealed no visible esophagitis. The frequency of heartburn was signific- antly associated with the presence of hiatal hernia but the frequency of reflux symptoms was not linked to the presence or severity of endoscopic lesions. Follow-up data > 2 month were available for 38 patients. Out of these 86.8% continued to have heartburn and 76.3% an acid taste after more than 2 months of treatment. The symptomatic response to PPI was significantly better (p0.05). 36% of patients reported a history of anxiety and depression but these disorders were not correlated with symptom frequency or response to PPI therapy. Conclusions: a) Frequency of GERD symptoms is not associated with severity of mucosal lesions; b) presence of a hiatal hernia is linked to more frequent symptoms; c) presence of a hiatal hernia predicts a favourable response to PPI therapy.Nora B. Zschau, William Tam, Jane M. Andrews, Richard H. Holloway, Mark Schoeman, Gerald J. Holtman