Global well-posedness for the 2D Boussinesq equations with zero viscosity

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• 作者：Daoguo Zhou ^{daoguozhou@hpu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zilai Li ; ^{lizl@hpu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Global existence ; Boussinesq equations ; Zero viscosity ; Bounded domain
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：1072-1079
• 全文大小：288 K

文摘

We prove the global well-posedness of the two-dimensional Boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data [class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306540&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306540&_rdoc=1&_issn=0022247X&md5=88a317008f4b986c6a20bc01847863d0" title="Click to view the MathML source">u₀∈L²class="mathContainer hidden">class="mathCode">$u_0\in L^2$, class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306540&_mathId=si15.gif&_user=111111111&_pii=S0022247X16306540&_rdoc=1&_issn=0022247X&md5=9f47a6d9f51b3f1e4034d1a347707993">class="imgLazyJSB inlineImage" height="15" width="92" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306540-si15.gif">class="mathContainer hidden">class="mathCode">$\mathrm{curl}{u}_0\in L^{\infty }$ and class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306540&_mathId=si22.gif&_user=111111111&_pii=S0022247X16306540&_rdoc=1&_issn=0022247X&md5=05e643382436fc059b4f6ce7d74770cc">class="imgLazyJSB inlineImage" height="21" width="86" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16306540-si22.gif">class="mathContainer hidden">class="mathCode">${\theta }_0\in B_{q,p}^{2-2/p}$ with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306540&_mathId=si23.gif&_user=111111111&_pii=S0022247X16306540&_rdoc=1&_issn=0022247X&md5=b1d76c7fd7136a1a0b43e4e1ad27f7a0" title="Click to view the MathML source">p∈(1,∞)class="mathContainer hidden">class="mathCode">$p\in (1,\infty )$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306540&_mathId=si24.gif&_user=111111111&_pii=S0022247X16306540&_rdoc=1&_issn=0022247X&md5=f5392d95f788779264a0ae004a3114b4" title="Click to view the MathML source">q∈(2,∞)class="mathContainer hidden">class="mathCode">$q\in (2,\infty )$]. Our method is based on the maximal regularity for heat equation.