带有科氏力的Navier-Stokes方程mild解的正则性

带有科氏力的Navier-Stokes方程mild解的正则性

李新新

李新新青岛大学数学与统计学院青岛266071

摘要:本文研究了三维空间中带有科氏力的Navier-Stokes方程的时间周期问题，证明了当外力属于Besov空间时，方程的周期mild解的正则性.

关键词：Navier-Stokes方程；mild解；正则性

参考文献

[1]P.Konieczny,andT.Yoneda,OndispersiveeffectoftheCoriolisforceforthestationaryNavier-Stokesequations,J.DifferentialEquations,250(2011),3859–3873.

[2]Y.Giga,K.Inui,A.Mahalov,andS.Matsui,Navier-StokesequationsinarotatingframeinR3withinitialdatanondecreasingatinfinity,HokkaidoMath.J.,35(2006),321–364.

[3]IwabuchiT,TakadaR.DispersiveeffectoftheCoriolisforceandlocalwell-posednessfortheNavier-StokesequationsintherotationalframeworkNCTAMpapers,NationalCongressofTheoreticalandAppliedMechanics,Japan.NationalCommitteeforIUTAM,2012:43-43.

[4]M.Hieber,Y.Shibata,TheFujita-KatoapproachtotheNavier-Stokesequationsintherotationalframework,Math.Z.,265(2010),481–491.

[5]H.Kozono,T.Ogawa,andY.Taniuchi,Navier-StokesequationsintheBesovspacenearL∞andBMO,KyushuJ.Math.,57(2003),303–324.

[6]A.MahalovandB.Nicolaenko,GlobalRegularityof3DRotatingNavier-StokesEquationsforResonantDomains,AppliedMathematicsLetters13(2000)51--57.

[7]HideoKozono,YukiMashikoandRyoTakada，ExistenceofperiodicsolutionsandtheirasymptoticstabilitytotheNavier–StokesequationswiththeCoriolisforce，J.Evol.Equ.2014SpringerBasel,DOI10.1007/s00028-014-0228-4

作者简介：李新新，女，山东聊城人，汉族，1990.08.06，青岛大学，数学科学与统计学院，研究生，应用数学，偏微分方程理论及其应用。