TY - JOUR
T1 - On the Generalized Porous Medium Equation in Fourier-Besov Spaces
AU - Xiao , Weiliang
AU - Zhou , Xuhuan
JO - Journal of Mathematical Study
VL - 3
SP - 316
EP - 328
PY - 2020
DA - 2020/05
SN - 53
DO - http://doi.org/10.4208/jms.v53n3.20.05
UR - https://global-sci.org/intro/article_detail/jms/16922.html
KW - Porous medium equation, well-posedness, blowup criterion, Fourier-Besov spaces.
AB - <p style="text-align: justify;">We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.</p>