Abstract
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-α equation (which replaces the solution u with (1-α2 L1)u for a Fourier Multiplier L) and the generalized Navier-Stokes equation (which replaces the viscosity term νδ with νL2). In this paper we consider the combination of these two equations, called the generalized Leray-α 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) based Sobolev space, the existence of a unique local solution with γ1+γ2>n/p+1. In the p=2 case, the local solution is extended to a global solution, improving on previously known results.
| Original language | English |
|---|---|
| Pages (from-to) | 102-116 |
| Number of pages | 15 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 136 |
| DOIs | |
| State | Published - May 1 2016 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
Global solutions to the generalized Leray-alpha equation with mixed dissipation terms. / Pennington, Nathan.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 136, 01.05.2016, p. 102-116.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Global solutions to the generalized Leray-alpha equation with mixed dissipation terms
AU - Pennington, Nathan
PY - 2016/5/1
Y1 - 2016/5/1
N2 - 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-α equation (which replaces the solution u with (1-α2 L1)u for a Fourier Multiplier L) and the generalized Navier-Stokes equation (which replaces the viscosity term νδ with νL2). In this paper we consider the combination of these two equations, called the generalized Leray-α 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) based Sobolev space, the existence of a unique local solution with γ1+γ2>n/p+1. In the p=2 case, the local solution is extended to a global solution, improving on previously known results.
AB - 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-α equation (which replaces the solution u with (1-α2 L1)u for a Fourier Multiplier L) and the generalized Navier-Stokes equation (which replaces the viscosity term νδ with νL2). In this paper we consider the combination of these two equations, called the generalized Leray-α 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) based Sobolev space, the existence of a unique local solution with γ1+γ2>n/p+1. In the p=2 case, the local solution is extended to a global solution, improving on previously known results.
UR - http://www.scopus.com/inward/record.url?scp=84959525624&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84959525624&partnerID=8YFLogxK
U2 - 10.1016/j.na.2016.02.006
DO - 10.1016/j.na.2016.02.006
M3 - Article
VL - 136
SP - 102
EP - 116
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
ER -