Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

Effectiveness of postoperative radiotherapy after radical cystectomy for locally advanced bladder cancer

BACKGROUND: Local-regional failure (LF) for locally advanced bladder cancer (LABC) after radical cystectomy (RC) is common even with chemotherapy and is associated with high morbidity/mortality. Postoperative radiotherapy (PORT) can reduce LF and may enhance overall survival (OS) but has no defined role. We hypothesized that the addition of PORT would improve OS in LABC in a large nationwide oncology database. METHODS: We identified ≥ pT3pN0-3M0 LABC patients in the National Cancer Database diagnosed 2004-2014 who underwent RC ± PORT. OS was calculated using Kaplan-Meier and Cox proportional hazards regression modeling was used to identify predictors of OS. Propensity matching was performed to match RC patients who received PORT vs those who did not. RESULTS: 15,124 RC patients were identified with 512 (3.3%) receiving PORT. Median OS was 20.0 months (95% CI, 18.2-21.8) for PORT vs 20.8 months (95% CI, 20.3-21.3) for no PORT (P = 0.178). In multivariable analysis, PORT was independently associated with improved OS: hazard ratio 0.87 (95% CI, 0.78-0.97); P = 0.008. A one-to-three propensity match yielded 1,858 patients (24.9% receiving PORT and 75.1% without). In the propensity-matched cohort, median OS was 19.8 months (95% CI, 18.0-21.6) for PORT vs 16.9 months (95% CI, 15.6-18.1) for no PORT (P = 0.030). In the propensity-matched cohort of urothelial carcinoma patients (N = 1,460), PORT was associated with improved OS for pT4, pN+, and positive margins (P \u3c 0.01 all). CONCLUSION: In this observational cohort, PORT was associated with improved OS in LABC. While the data should be interpreted cautiously, these results lend support to the use of PORT in selected patients with LABC, regardless of histology. Prospective trials of PORT are warranted

Intravesical rAd-IFNα/Syn3 for Patients With High-Grade, Bacillus Calmette-Guerin-Refractory or Relapsed Non-Muscle-Invasive Bladder Cancer: A Phase II Randomized Study.

Purpose Many patients with high-risk non-muscle-invasive bladder cancer (NMIBC) are either refractory to bacillus Calmette-Guerin (BCG) treatment or may experience disease relapse. We assessed the efficacy and safety of recombinant adenovirus interferon alfa with Syn3 (rAd-IFNα/Syn3), a replication-deficient recombinant adenovirus gene transfer vector, for patients with high-grade (HG) BCG-refractory or relapsed NMIBC. Methods In this open-label, multicenter (n = 13), parallel-arm, phase II study ( ClinicalTrials.gov identifier: NCT01687244), 43 patients with HG BCG-refractory or relapsed NMIBC received intravesical rAd-IFNα/Syn3 (randomly assigned 1:1 to 1 × 10(11) viral particles (vp)/mL or 3 × 10(11) vp/mL). Patients who responded at months 3, 6, and 9 were retreated at months 4, 7, and 10. The primary end point was 12-month HG recurrence-free survival (RFS). All patients who received at least one dose were included in efficacy and safety analyses. Results Forty patients received rAd-IFNα/Syn3 (1 × 10(11) vp/mL, n = 21; 3 × 10(11) vp/mL, n = 19) between November 5, 2012, and April 8, 2015. Fourteen patients (35.0%; 90% CI, 22.6% to 49.2%) remained free of HG recurrence 12 months after initial treatment. Comparable 12-month HG RFS was noted for both doses. Of these 14 patients, two experienced recurrence at 21 and 28 months, respectively, after treatment initiation, and one died as a result of an upper tract tumor at 17 months without a recurrence. rAd-IFNα/Syn3 was well tolerated; no grade four or five adverse events (AEs) occurred, and no patient discontinued treatment because of an adverse event. The most frequently reported drug-related AEs were micturition urgency (n = 16; 40%), dysuria (n = 16; 40%), fatigue (n = 13; 32.5%), pollakiuria (n = 11; 28%), and hematuria and nocturia (n = 10 each; 25%). Conclusion rAd-IFNα/Syn3 was well tolerated. It demonstrated promising efficacy for patients with HG NMIBC after BCG therapy who were unable or unwilling to undergo radical cystectomy