简介:ForquantumfluidsgovernedbythecompressiblequantumNavier-StokesequationsinR~3withviscosityandheatconduction,weprovetheoptimalL~p-L~qdecayratesfortheclassicalsolutionsnearconstantstates.TheproofisbasedonthedetailedlinearizeddecayestimatesbyFourieranalysisoftheoperators,whichisdrasticallydifferentfromthecasewhenquantumeffectsareabsent.
简介:Thispaperisconcernedwiththelarge-timebehaviorofsolutionstoaninitial-boundary-valueproblemforfullcompressibleNavier-Stokesequationsonthehalfline(0,∞),whichisnamedimpermeablewallproblem.Itisshownthatthe3-rarefactionwaveisstableunderpartiallylargeinitialperturbationiftheadiabaticexponentγiscloseto1.Herepartiallylargeinitialperturbationmeansthattheperturbationofabsolutetemperatureissmall,whiletheperturbationsofspecificvolumeandvelocitycanbelarge.Theproofisgivenbytheelementaryenergymethod.
简介:考虑一类Navier-Stokes-Smoluchowski方程组在有界光滑区域Ω?R3中的初边值问题.利用Ballew在其博士论文中得到的局部强解,对强解建立一系列与时间无关的先验估计,最后得到此模型的整体强解.
简介:Inthispaper,westudytheCauchyproblemforthe3DgeneralizedNavier-Stokes-Boussinesqequationswithfractionaldiffusion:{ut+(u·▽)u+v∧2αu=-▽p+θe(3),e3=(0,0,1)T,θt+(u·▽)θ=0,Dicu=0.Withthehelpofthesmoothingeffectofthefractionaldiffusionoperatorandalogarithmicestimate,weprovetheglobalwell-posednessforthissystemwithα≥5/4.Moreover,theuniquenessandcontinuityofthesolutionwithweakerinitialdataisbasedonFourierlocalizationtechnique.Ourresultsextendonesonthe3DNavier-Stokesequationswithfractionaldiffusion.
简介:分别从布朗运动的主方程和连续时间随机游走模型出发导出了经典的扩散方程。进一步,在加入了外力场后,得到了Fokker-Planck方程,并对描述次扩散现象的分数阶扩散方程的导出进行了研究。