Unconditional uniqueness of solution for critical NLS in high dimensions

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• 作者：Jing Lu^a ; ^{lujing326@126.com" class="auth_mail" title="E-mail the corresponding author} ; Yushun Xu^b ; ^{xys_651@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Unconditional uniqueness ; Paraproduct estimates ; Besov spaces ; Nonlinear Schrö ; dinger equation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：436
• 期：2
• 页码：1214-1222
• 全文大小：305 K

文摘

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15010203&_mathId=si1.gif&_user=111111111&_pii=S0022247X15010203&_rdoc=1&_issn=0022247X&md5=b084542f69183d3a577421a46f81429f">class="imgLazyJSB inlineImage" height="15" width="28" 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-S0022247X15010203-si1.gif">class="mathContainer hidden">class="mathCode">${\dot{H}}^{s_c}$ (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15010203&_mathId=si2.gif&_user=111111111&_pii=S0022247X15010203&_rdoc=1&_issn=0022247X&md5=65edbfd337ef0e35f7a9805f195b0a78" title="Click to view the MathML source">0≤s_c<1class="mathContainer hidden">class="mathCode">$0\le s_c<1$) critical nonlinear Schrödinger equations (NLS). By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15010203&_mathId=si3.gif&_user=111111111&_pii=S0022247X15010203&_rdoc=1&_issn=0022247X&md5=1d1a400daa8a95d18f0f35e338b39d7c">class="imgLazyJSB inlineImage" height="19" width="105" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X15010203-si3.gif">class="mathContainer hidden">class="mathCode">$C_t(I;{\dot{H}}^{s_c}({\mathbb{R}}^d))$ for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15010203&_mathId=si4.gif&_user=111111111&_pii=S0022247X15010203&_rdoc=1&_issn=0022247X&md5=7b05f33a28f7f1a8c3e981a59eceaf70" title="Click to view the MathML source">d≥6class="mathContainer hidden">class="mathCode">$d\ge 6$. This extends earlier results by Yin Yin Su Win and Y. Tsutsumi [19] and Cazenave [3].