کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
839348 | 1470465 | 2016 | 15 صفحه PDF | دانلود رایگان |

Due to the intractability of the Navier–Stokes equation, it is common to study approximating equations. Two of the most common of these are the Leray-αα equation (which replaces the solution uu with (1−α2L1)u(1−α2L1)u for a Fourier Multiplier LL) and the generalized Navier–Stokes equation (which replaces the viscosity term ν△ν△ with νL2νL2). In this paper we consider the combination of these two equations, called the generalized Leray-αα equation. We provide a brief outline of the typical strategies used to solve such equations, and prove, with initial data in a low-regularity Lp(Rn)Lp(Rn) based Sobolev space, the existence of a unique local solution with γ1+γ2>n/p+1γ1+γ2>n/p+1. In the p=2p=2 case, the local solution is extended to a global solution, improving on previously known results.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 136, May 2016, Pages 102–116