Global classical solutions of the full compressible Navier-Stokes equations with cylindrical or spherical symmetry

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• 作者：Xinhua Zhao ^{xinhuazhao211@163.com" class="auth_mail" title="E-mail the corresponding author} ; Lei Yao ; ^{yaolei1056@hotmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Full compressible Navier&ndash ; Stokes equations ; Cylindrical or spherical symmetry ; Global classical solutions ; Weighted estimates
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：Complete
• 页码：139-167
• 全文大小：796 K

文摘

In this paper, we consider the full compressible Navier–Stokes equations in mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si1.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=a568fb5d436c2a74eaf4727f0c70f51f" title="Click to view the MathML source">NmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">Nmath>(mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si2.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=970e91f3784e66cf32d86795abc4bcd7" title="Click to view the MathML source">N≥2mathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">N≥2math>) space dimension with cylindrical or spherical symmetric initial data. The global existence of strong and classical solutions is established. The analysis is based on some delicate a priori   estimates which depend on the assumption mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si3.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=01f434e8d3cbe706844dbeb820ba6bef" title="Click to view the MathML source">κ(θ)=θ^qmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">κ(θ)=θqmath> where mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si4.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=2c63c36eff4d2a99c761cdc898dead2b" title="Click to view the MathML source">q⩾0mathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll">q⩾0math> and mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si5.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=e4afc4c1831ca38dbd8e37c3bcea0cbf">mage" height="18" width="223" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S146812181630058X-si5.gif">mathContainer hidden">mathCode"><math altimg="si5.gif" overflow="scroll">(ρ0,θ0)∈H2,(u0,v0,w0)∈H01∩H2math>. Compared with the results in Wen and Zhu (2014) and Qin, Yang, Yao and Zhou (2015), our results relax the restriction mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si6.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=67b6ebe6f685a82b3858edfb75928ab2" title="Click to view the MathML source">q>0mathContainer hidden">mathCode"><math altimg="si6.gif" overflow="scroll">q>0math>, when there is no initial vacuum and include the global existence of classical solutions for both the cylindrical or spherical symmetric cases, respectively. It should point out that we obtain the global classical solutions with the help of weighted mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si7.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=16a1a23c0125549034791b5657984edf" title="Click to view the MathML source">H³mathContainer hidden">mathCode"><math altimg="si7.gif" overflow="scroll">H3math> estimates of mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630058X&_mathId=si8.gif&_user=111111111&_pii=S146812181630058X&_rdoc=1&_issn=14681218&md5=99930ba861687a9c10381aff51089309" title="Click to view the MathML source">(u,v,w,θ)mathContainer hidden">mathCode"><math altimg="si8.gif" overflow="scroll">(u,v,w,θ)math>.