On Leray's Problem for Almost Periodic Flows

Berselli Luigi C.; Romito Marco

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On Leray's Problem for Almost Periodic Flows

机译：关于Leray的概周期流问题

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Weproveexistenceanduniquenessforfully-developed(Poiseuille-type)flowsinsemi-infinitecylinders,inthesettingof(time)almost-periodicfunctions.InthecaseofStepanovalmost-periodicfunctionstheproofisbasedonadetailedvariationalanalysisofalinear``inverse''problem,whileintheBesicovitchsettingtheprooffollowsbyapreciseanalysisinwave-numbers.Next,weuseourresultstoconstructauniquealmostperiodicsolutiontothesocalled``Leray'sproblem''concerning3Dfluidmotionintwosemi-infinitecylindersconnectedbyaboundedreservoir.InthecaseofStepanovfunctionsweneedanaturalrestrictiononthesizeoftheflux(withrespecttotheviscosity),whileforBesicovitchsolutionscertainlimitationsonthegeneralisedFouriercoefficientsarerequested.

机译：Weproveexistenceanduniquenessforfully开发（泊肃叶型）flowsinsemi-infinitecylinders，inthesettingof（时间）几乎periodicfunctions.InthecaseofStepanovalmost-periodicfunctionstheproofisbasedonadetailedvariationalanalysisofalinear``inverse''problem，whileintheBesicovitchsettingtheprooffollowsbyapreciseanalysisinwave-numbers.Next，weuseourresultstoconstructauniquealmostperiodicsolutiontothesocalled``Leray'sproblem''concerning3Dfluidmotionintwosemi-infinitecylindersconnectedbyaboundedreservoir.InthecaseofStepanovfunctionsweneedanaturalrestrictiononthesizeoftheflux（相对于粘度），同时要求对Besicovitch解决方案确定通用傅立叶系数的某些限制。

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《Journal of mathematical sciences, The University of Tokyo》 |2012年第1期|共页
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Berselli Luigi C.; Romito Marco;
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1. Erratum to: Time-Periodic Solutions of the Navier-Stokes Equations in Unbounded Cylindrical Domains - Leray's Problem for Periodic Flows (Rational Mech. Anal., (2005), 178, (301-325), 10.1007/s00205-005-0376-3) [J] . da Veiga H.B. Archive for Rational Mechanics and Analysis . 2010,第3期

机译：勘误表：无界圆柱域中Navier-Stokes方程的时间周期解-周期性流动的Leray问题（Rational Mech。Anal。，（2005），178，（301-325），10.1007 / s00205-005-0376- 3）
2. Time-periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains - Leray's problem for periodic flows [J] . Da Veiga HB Archive for Rational Mechanics and Analysis . 2005,第3期

机译：无界圆柱域中Navier-Stokes方程的时间周期解-周期流的Leray问题
3. Time-Periodic Solutions of the Navier-Stokes Equations in Unbounded Cylindrical Domains – Leray's Problem for Periodic Flows [J] . H. Beirão da Veiga Archive for Rational Mechanics and Analysis . 2005,第3期

机译：无界圆柱域中Navier-Stokes方程的时间周期解—周期流的Leray问题
4. PERIODIC PATTERNED CONTROL AND PERIODIC OUTPUT FLOWS [C] . Collart Dutilleul Simon, Denat Jean-Paul, International Federation of Automatic Control, IFAC Symposium on Large Scale Systems . 2002

机译：定期图案化控制和周期性输出流动
5. Controlling mixing and segregation in time periodic granular flows. [D] . Bhattacharya, Tathagata. 2011

机译：控制时间周期颗粒流中的混合和分离。
6. Second Leray spectral sequence of relative hypercohomology [O] . Saul Lubkin, Goro C. Kato 1978

机译：相对超同源性的第二Leray光谱序列
7. Time periodic solutions of the Navier-Stokes equations in unbounded cylindrical domains—Leray’s problem for periodic flows [O] . H. Beirão Da Veiga 2015

机译：无界圆柱域中Navier-stokes方程的时间周期解 - Leray的周期流问题

On Leray's Problem for Almost Periodic Flows

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