论文标题
BESOV空间中双曲线Keller-Segel模型的不适性
Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces
论文作者
论文摘要
在本文中，我们在b^σ_{p，\ infty} $中提供了新的$ u_0 \的新结构，以使从$ u_0 $开始的双曲线凯勒 - 塞格尔模型的相应解决方案不连续$ t = 0 $ in $ t = 0 $ in $ b^σ_ p \ leq \ infty $，这意味着在$ b^σ_{p，\ infty} $中的该方程的不良性。我们的结果概括了\ cite {zhang01}（J. Dill.Ed.334（2022））中的最新工作，其中考虑了$ d = 1 $和$ p = 2 $的情况。
In this paper, we give a new construction of $u_0\in B^σ_{p,\infty}$ such that the corresponding solution to the hyperbolic Keller-Segel model starting from $u_0$ is discontinuous at $t = 0$ in the metric of $B^σ_{p,\infty}(\R^d)$ with $d\geq1$ and $1\leq p\leq\infty$, which implies the ill-posedness for this equation in $B^σ_{p,\infty}$. Our result generalizes the recent work in \cite{Zhang01} (J. Differ. Equ. 334 (2022)) where the case $d=1$ and $p=2$ was considered.
