论文标题
对麝香问题的新重新重新制定，表面张力
A new reformulation of the Muskat problem with surface tension
论文作者
论文摘要
将双层潜力的衍生物和相关的奇异积分运算符连接起来的两个密度$ \ vartheta $与这些操作员的$ l_2 $ -adjoints相关的相关奇异积分运算符的两个公式，用于重新估算表面紧张和不合格的$ nontine of-line of-line of-line cormecosities的$ l_2 $ adjoints，用于重新塑造。这些操作员。该公式的一个优点是非线性现在是衍生品。然后利用此方面和抽象的准抛物线理论来建立所有亚临界Sobolev Spaces $ W^S_P（\ Mathbb {r}）$，并使用$ p \ in（1，\ infty）$和$ s \ in（1+1/p，2）$。
Two formulas that connect the derivatives of the double layer potential and of a related singular integral operator evaluated at some density $\vartheta$ to the $L_2$-adjoints of these operators evaluated at the density $\vartheta'$ are used to recast the Muskat problem with surface tension and general viscosities as a system of equations with nonlinearities expressed in terms of the $L_2$-adjoints of these operators. An advantage of this formulation is that the nonlinearities appear now as a derivative. This aspect and abstract quasilinear parabolic theory are then exploited to establish a local well-posedness result in all subcritical Sobolev spaces $W^s_p(\mathbb{R})$ with $p\in(1,\infty)$ and $s\in (1+1/p,2)$.
