论文标题
在亚临界$ l_p $ -sobolev空间中，表面张力和平等粘度的麝香问题
The Muskat problem with surface tension and equal viscosities in subcritical $L_p$-Sobolev spaces
论文作者
论文摘要
在本文中，我们确定了马斯卡特问题的体积良好，表面张力和相等的粘度在sobolev space $ w^s_p（\ mathbb {r}）$中，其中$ {p \ in（1,2]} $和$ {s \ in（1+1/p，2）$。抛物线进化问题$ w^{\叠加{s} -2} _p（\ mathbb {r}）$，其中$ {\ overline {s} \ in（1+1/p，s）} $，我们证明解决方案会立即变得平稳，我们为解决方案提供了标准。
In this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $W^s_p(\mathbb{R})$, where ${p\in(1,2]}$ and ${s\in(1+1/p,2)}$. This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $W^{\overline{s}-2}_p(\mathbb{R})$, where ${\overline{s}\in(1+1/p,s)}$. Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.
