arXiv subjects

Xuhuan Zhou

Publications and source records attributed to Xuhuan Zhou.

2 recordsLinked to original sources

arXiv2016

Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces

The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^α$ with nonnegative initial data, $α>\frac d2+1$. Besides, we correct a mistake in our previous paper \cite{zhou01}.

math.AP↗

arXiv2016

On the generalized porous medium equation in Fourier-Besov spaces

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: $u_t+νΛ^βu=\nabla\cdot(u\nabla Pu)$, 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.

math.AP↗