Multiple Elliptic Equations And Navier-stokes Radial Solutions Of Regular Solution Equation

This paper introduces the historical background of elliptic equations and development and a class of equations with singular source of Laplace research and development. Introduction and development of fluid dynamics fractiona Navier-stokes equation of stateThe following chapter we discuss elliptic equations -Δu=λk(|x|)f(u) with initial value of theExistence of Radial Solutions, This chapter uses a cone fixed point theorem and the clever use of a convex functionWere proved f(u) and k(|x|) to satisfy certain conditions and situations, and u satisfy the boundary value problem, the obtained equation by at least one positive term solution, and with the boundary value on the existence of radial solutions for triple the results.The third chapter,we discuss the fractional dissipation of the NS equations (?)lu+u·▽u+▽p=-(-Δ)αu as the regular solution.then use the Holder inequality, the Gagliardo-Nirenberg,Young inequality, Gronwall inequality proved Proved that if 0<α≤5/4 and 1/2<α≤5/4 when, respectively, the velocity field gradient of any two components belong to a space, a weak solution of the equation is regularity in the (0, T] of the results.