In this paper, we study the radial symmetry properties of stationary and uniformlyrotating solutions of the 2D Euler and gSQG equations, both in the smooth setting and the patch setting. For the 2D Euler equation, we show that any smooth stationary solution with compactly supported and nonnegative vorticity must be radial, without any assumptions on the connectedness of the support or the level sets. In the patch setting, for the 2D Euler equation we show that every uniformly-rotating patch D with angular velocity Ω ≤ 0 or Ω ≥ 1 2 must be radial, where both bounds are sharp. For the gSQG equation we obtain a similar symmetry result for Ω ≤ 0 or Ω ≥ Ωα (with the bounds being sharp), under the additional assumption that the patch is simply-connected. These results settle several open questions in Hmidi [48] and de la Hoz-Hassainia-Hmidi-Mateu [28] on uniformly-rotating patches. Along the way, we close a question on overdetermined problems for the fractional Laplacian [22, Remark 1.4], which may be of independent interest. The main new ideas come from a calculus of variations point of view.

In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $$\Omega $$ Ω , such that it has positive vorticity and is concentrated in a finite disjoint union of smooth curves with finite length is the trivial one: constant vorticity amplitude supported on a union of nested, concentric circles. The proof follows a desingularization argument and a calculus of variations flavor.

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/npsi/ctrl?lang=en http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?lang=fr Access and use of this website and the material on it are subject to the Terms and Conditions set forth at http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/jsp/nparc_cp.jsp?lang=en NRC Publications Archive Archives des publications du CNRCThis publication could be one of several versions: author's original, accepted manuscript or the publisher's version. / La version de cette publication peut être l'une des suivantes : la version prépublication de l'auteur, la version acceptée du manuscrit ou la version de l'éditeur. For the publisher's version, please access the DOI link below./ Pour consulter la version de l'éditeur, utilisez le lien DOI ci-dessous.http://dx.doi.org/10.1016/j.ins. 2009.01.038 Information Sciences, 179, 15, pp. 2606Sciences, 179, 15, pp. -2617Sciences, 179, 15, pp. , 2009 A service-oriented city portal framework and collaborative development platform Zhu, D.; Li, Y.; Xu, Y.; Shi, J.; Shen, W. The material in this document is covered by the provisions of the Copyright Act, by Canadian laws, policies, regulations and international agreements. Such provisions serve to identify the information source and, in specific instances, to prohibit reproduction of materials without written permission. For more information visit http://laws.justice.gc.ca/en/showtdm/cs/C-42Les renseignements dans ce document sont protégés par la Loi sur le droit d'auteur, par les lois, les politiques et les règlements du Canada et des accords internationaux. Ces dispositions permettent d'identifier la source de l'information et, dans certains cas, d'interdire la copie de documents sans permission écrite. Abstract: Cities are being equipped with multiple information systems to provide public services for city officials, officers, and citizens. There are problems with efficient service implementation and provision, e.g., data islands and function overlaps between systems and applications. Service-oriented portals are efficient at facilitating information sharing and collaborative work between city systems and users. The goal is to make cities responsive, agile and to provide composite services efficiently and cost efficiently. A service-oriented framework for city portals is proposed to design, integrate and streamline city systems and applications. A model-driven collaborative development platform is developed for service-oriented digital portals of the proposed framework. The architecture and implementation issues of the platform are discussed. The service identification policies are discussed within the framework. A case study has been developed and evaluated on the platform to provide a composite service, i.e., a traffic search service on a city portal.

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