| | |
| | |
Stat |
Members: 3667 Articles: 2'599'751 Articles rated: 2609
09 February 2025 |
|
| | | |
|
Article overview
| |
|
Well-posedness and Gevrey Analyticity of the Generalized Keller-Segel System in Critical Besov Spaces | Jihong Zhao
; | Date: |
1 Aug 2015 | Abstract: | In this paper, we study the Cauchy problem for the generalized Keller-Segel
system with the cell diffusion being ruled by fractional diffusion:
egin{equation*} egin{cases}
partial_{t}u+Lambda^{alpha}u-
ablacdot(u
abla psi)=0quad &mbox{in}
mathbb{R}^n imes(0,infty),
-Delta psi=uquad &mbox{in}
mathbb{R}^n imes(0,infty),
u(x,0)=u_0(x), &mbox{in} mathbb{R}^n. end{cases} end{equation*} In
the case that $1<alphaleq 2$, we prove local well-posedness for any initial
data and global well-posedness for small initial data in critical Besov spaces
$dot{B}^{-alpha+frac{n}{p}}_{p,q}(mathbb{R}^{n})$ with $1leq p<infty$,
$1leq qleq infty$, and analyticity of solutions for initial data $u_{0}in
dot{B}^{-alpha+frac{n}{p}}_{p,q}(mathbb{R}^{n})$ with $1< p<infty$, $1leq
qleq infty$. Moreover, the global existence and analyticity of solutions with
small initial data in critical Besov spaces
$dot{B}^{-alpha}_{infty,1}(mathbb{R}^{n})$ is also established. In the
limit case that $alpha=1$, we prove global well-posedness for small initial
data in critical Besov spaces $dot{B}^{-1+frac{n}{p}}_{p,1}(mathbb{R}^{n})$
with $1leq p<infty$ and $dot{B}^{-1}_{infty,1}(mathbb{R}^{n})$, and show
analyticity of solutions for small initial data in
$dot{B}^{-1+frac{n}{p}}_{p,1}(mathbb{R}^{n})$ with $1<p<infty$ and
$dot{B}^{-1}_{infty,1}(mathbb{R}^{n})$, respectively. | Source: | arXiv, 1508.0117 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|