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 d="mmlsi1" class="mathmlsrc">text 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">Ndden">de">$N$(d="mmlsi2" class="mathmlsrc">text 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≥2dden">de">$N\ge 2$) 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 d="mmlsi3" class="mathmlsrc">text 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^qdden">de">$\kappa \left(\theta \right)={\theta }^q$ where d="mmlsi4" class="mathmlsrc">text 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⩾0dden">de">$q⩾0$ and d="mmlsi5" class="mathmlsrc">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">dth="223" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S146812181630058X-si5.gif">dden">de">$({\rho }_0,{\theta }_0)\in H^2,(u_0,v_0,w_0)\in H_0^1\cap H^2$. Compared with the results in Wen and Zhu (2014) and Qin, Yang, Yao and Zhou (2015), our results relax the restriction d="mmlsi6" class="mathmlsrc">text 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>0dden">de">$q>0$, 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 d="mmlsi7" class="mathmlsrc">text 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">H³dden">de">$H^3$ estimates of d="mmlsi8" class="mathmlsrc">text 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)dden">de">$(u,v,w,\theta )$.