This article is devoted to the study of Cauchy problem for Muskat equation. We consider initial data belonging critical Sobolev space functions with three-half derivative in L2, up a fractional logarithmic correction. As corollary, we obtain first local and global well-posedness results free surfaces which are not Lipschitz.

The digital gates are basic electronic component of any digital circuit. Digital circuit should be simplified in order to reduce its cost by reducing number of digital gates required to implement it. To achieve this, we use Boolean expression that helps in obtaining minimum number of terms and does not contain any redundant pair. Karnaugh map (K-map) and Quine-McCluskey (QM) methods are well kn...