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

详细信息    查看全文

• 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 class="mathmlsrc">class="formulatext stixSupport 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">Nclass="mathContainer hidden">class="mathCode">$N$(class="mathmlsrc">class="formulatext stixSupport 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≥2class="mathContainer hidden">class="mathCode">$N\ge 2$) 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 class="mathmlsrc">class="formulatext stixSupport 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^qclass="mathContainer hidden">class="mathCode">$\kappa \left(\theta \right)={\theta }^q$ where class="mathmlsrc">class="formulatext stixSupport 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⩾0class="mathContainer hidden">class="mathCode">$q⩾0$ and class="mathmlsrc">title="View the MathML source" class="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">class="imgLazyJSB inlineImage" 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">class="mathContainer hidden">class="mathCode">. Compared with the results in Wen and Zhu (2014) and Qin, Yang, Yao and Zhou (2015), our results relax the restriction class="mathmlsrc">class="formulatext stixSupport 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>0class="mathContainer hidden">class="mathCode">$q>0$, 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 class="mathmlsrc">class="formulatext stixSupport 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">H³class="mathContainer hidden">class="mathCode">$H^3$ estimates of class="mathmlsrc">class="formulatext stixSupport 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)class="mathContainer hidden">class="mathCode">$(u,v,w,\theta )$.