This paper is devoted to the study of solutions with critical regularity for two-dimensional Muskat equation. We prove that Cauchy problem well-posed on endpoint Sobolev space $$L^2$$ functions three-half derivative in . result optimal respect scaling One well-known difficulty one cannot define a flow map such lifespan bounded from below subsets this space. To overcome this, we estimate norm wh...

In this paper, we establish some new endpoint regularity properties of multilinear maximal operators and their fractional variants, both in the centered uncentered cases. The main results obtain not only answer a question Liu, Wu, Xue Yabuta, but also provide Sobolev boundedness continuity for operators. More importantly, present approach to deal with above

in this paper, non-polynomial spline method for solving coupled burgers’ equations are presented. we take a new spline function. the stability analysis using von-neumann technique shows the scheme is unconditionally stable. to test accuracy the error norms2l, ∞l are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equatio...

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

cobalt is one of the most important constituent present in ceramic industries. glazers are the relevant workers when they are producing blue colored ceramic, causing occupational exposure to such metal. through this study, urinary cobalt was determined in glazers in a ceramic industry when they were producing blue-colored ceramic glazes.in this case-control study, spot urine samples were collec...