On the Generalized Porous Medium Equation in Fourier-Besov Spaces (Journal of Mathematical Study, 2020)
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: $u_t+ u Λ^{β}u= abla·(u abla Pu)$, 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.
Keywords: Porous medium equation; well-posedness; blowup criterion; Fourier-Besov spaces.