Academic Journal
Circular flows for the Euler equations in two-dimensional annular domains, and related free boundary problems
| العنوان: | Circular flows for the Euler equations in two-dimensional annular domains, and related free boundary problems |
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| المؤلفون: | Hamel, François, Nadirashvili, Nikolai |
| المساهمون: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0013,NONLOCAL,Phénomènes de propagation et équations non locales(2014), European Project: 321186,EC:FP7:ERC,ERC-2012-ADG_20120216,READI(2013) |
| المصدر: | ISSN: 1435-9855. |
| بيانات النشر: | HAL CCSD European Mathematical Society |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | Euler equations, circular flows, semilinear elliptic equations, free boundary problems, method of moving planes AMS 2010 Classification: 35B06, 35B50, 35B53, 35J61, 76B03, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| الوصف: | International audience ; In this paper, we firstly consider steady Euler flows in two-dimensional bounded annuli, as well as in complements of disks, in punctured disks and in the punctured plane. We prove that, if the flow does not have any stagnation point and satisfies rigid wall boundary conditions together with further conditions at infinity in the case of unbounded domains and at the center in the case of punctured domains, then the flow is circular, namely the streamlines are concentric circles. In other words, the flow then inherits the radial symmetry of the domain. We secondly show two classification results for the steady Euler equations in simply or doubly connected bounded domains with free boundaries. Here, the flows are further assumed to have constant norm on each connected component of the boundary, and the domains are then proved to be disks or annuli. On the one hand, the proofs use ODE and PDE arguments to establish some geometric properties of the trajectories of the flow and the orthogonal trajectories of the gradient of the stream function. On the other hand, we also show some comparison results of independent interest for a derived semilinear elliptic equation satisfied by the stream function. These last results, which are based on the method of moving planes, adapted here to some almost circular domains located between some streamlines of the flow, lead with a limiting argument to the radial symmetry of the stream function and the streamlines of the flow. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | info:eu-repo/semantics/altIdentifier/arxiv/1909.01666; info:eu-repo/grantAgreement/EC/FP7/321186/EU/Reaction-Diffusion Equations, Propagation and Modelling/READI; hal-02277176; https://hal.science/hal-02277176; https://hal.science/hal-02277176v2/document; https://hal.science/hal-02277176v2/file/hamel-nadirashvili.pdf; ARXIV: 1909.01666 |
| DOI: | 10.4171/JEMS/1177 |
| الاتاحة: | https://hal.science/hal-02277176 https://hal.science/hal-02277176v2/document https://hal.science/hal-02277176v2/file/hamel-nadirashvili.pdf https://doi.org/10.4171/JEMS/1177 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.B0986C2E |
| قاعدة البيانات: | BASE |
| DOI: | 10.4171/JEMS/1177 |
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