PARTIAL REGULARITY FOR THE NAVIER-STOKES-FOURIER SYSTEM

(整期优先)网络出版时间:2011-05-15
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Thispaperaddressesanonstationaryflowofheat-conductiveincompressibleNewtonianfluidwithtemperature-dependentviscositycoupledwithlinearheattransferwithadvectionandaviscousheatsourceterm,underNavier/Dirichletboundaryconditions.Thepartialregularityforthevelocityofthefluidisprovedforeachproperweaksolution,thatis,forsuchweaksolutionswhichsatisfysomelocalenergyestimatesinasimilarwaytothesuitableweaksolutionsoftheNavier-Stokessystem.Finally,westudythenatureofthesetofpointsinspaceandtimeuponwhichproperweaksolutionscouldbesingular.