Note on the weak-strong uniqueness criterion for the β-QG in Morrey-Campanato space

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• 作者：Saddek Gala ; ^a ; ^{sadek.gala@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{sgala@ksu.edu.sa" class="auth_mail" title="E-mail the corresponding author} ; ^{gala.sadek@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Maria Alessandra Ragusa^b ; ^{maragusa@dmi.unict.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quasi-geostrophic equation ; Weak&ndash ; strong uniqueness criterion ; Morrey&ndash ; Campanato space
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：293
• 期：Complete
• 页码：65-71
• 全文大小：326 K

文摘

Consider the β  -quasi-geostrophic equations with the initial data θ₀∈L²(R²)${\theta }_0\in L^2\left({\mathbb{R}}^2\right)$. Let θ   and $\tilde{\theta }$ be two weak solutions with the same initial value θ₀. If θ satisfies the energy inequality and ifwhere ${\stackrel{.}{\mathcal{M}}}_{p,q}\left({\mathbb{R}}^2\right)$ denotes the homogeneous Morrey–Campanato space, then we have $\theta =\tilde{\theta }$. Due to the embedding relation $L^p\left({\mathbb{R}}^2\right)\subset {\stackrel{.}{\mathcal{M}}}_{p,q}\left({\mathbb{R}}^2\right)$ with 1 < p < q < ∞, we see that our result is an improvement of the corresponding result given by Zhao and Liu (2013).