http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
DERIVATION OF THE g-NAVIER-STOKES EQUATIONS
Jaiok Roh 충청수학회 2006 충청수학회지 Vol.19 No.3
The 2D g-Navier-Stokes equations are a certain modified Navier-Stokes equations and have the following form, ∂u ∂t − ν∆u + (u · ∇)u + ∇p = f , in Ω with the continuity equation ∇ · (gu) = 0, in Ω, where g is a suitable smooth real valued function. In this paper, we will derive 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In addition, we will see the relationship between two equations.
Jaiok Roh 충청수학회 2006 충청수학회지 Vol.19 No.3
. Roh[1] derived 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In this paper, we will see the space L 2 (Ω, g), which is the weighted space of L 2 (Ω), as natural generalized space of L 2 (Ω) which is mathematical setting for Navier-Stokes equations. Our future purpose is to use the space L 2 (Ω, g) as mathematical setting for the g-Navier-Stokes equations. In addition, we will see Helmoltz-Leray projection on L 2p er (Ω, g) and compare with the one on L 2p er (Ω).RP
GEOMETRY OF L<SUP>2</SUP>(Ω, g)
Roh, Jaiok 충청수학회 2006 충청수학회지 Vol.19 No.3
Roh[1] derived 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In this paper, we will see the space $L^2({\Omega},\;g)$, which is the weighted space of $L^2({\Omega})$, as natural generalized space of $L^2({\Omega})$ which is mathematical setting for Navier-Stokes equations. Our future purpose is to use the space $L^2({\Omega},\;g)$ as mathematical setting for the g-Navier-Stokes equations. In addition, we will see Helmoltz-Leray projection on $L^2_{per}({\Omega},\;g)$) and compare with the one on $L^2_{per}({\Omega})$.
DERIVATION OF THE g-NAVIER-STOKES EQUATIONS
Roh, Jaiok 충청수학회 2006 충청수학회지 Vol.19 No.3
The 2D g-Navier-Stokes equations are a certain modified Navier-Stokes equations and have the following form, $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla})u+{\nabla}p=f$$, in ${\Omega}$ with the continuity equation ${\nabla}{\cdot}(gu)=0$, in ${\Omega}$, where g is a suitable smooth real valued function. In this paper, we will derive 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In addition, we will see the relationship between two equations.
Asymptotic aspect of derivations in Banach algebras
Roh, Jaiok,Chang, Ick-Soon Springer International Publishing 2017 Journal of inequalities and applications Vol.2017 No.1
<P>We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.</P>
Approximation by First-Order Linear Differential Equations with an Initial Condition
Roh, Jaiok,Jung, Soon-Mo Hindawi Limited 2016 Journal of function spaces Vol.2016 No.-
<P>We will consider a continuously differentiable functiony:I→Rsatisfying the inequalitypt<SUP>y′</SUP>t-qtyt-rt≤εfor allt∈Iandy<SUB>t0</SUB>-α≤δfor some<SUB>t0</SUB>∈Iand someα∈R. Then we will approximateyby a solutionzof the linear equationpt<SUP>z′</SUP>t-qtzt-r(t)=0withz(<SUB>t0</SUB>)=α.</P>
The properties of the solutions of the incompressible flows on an exterior domain
Elsevier 2018 APPLIED MATHEMATICS LETTERS Vol.84 No.-
<P><B>Abstract</B></P> <P>In this paper, we want to see the properties of the smooth solutions u of the incompressible flows on an exterior domain Ω of <SUP> R 2 </SUP> . Specially, when the vorticity ω = ∇ × u has a bounded support, with suitable conditions we will show that there exists a constant C ( p , q ) such that <SUB> ∥ u ∥ <SUP> L p </SUP> ( Ω ) </SUB> ≤ C <SUB> ∥ u ∥ <SUP> L q </SUP> ( Ω ) </SUB> for 1 < p ≤ q ≤ ∞ .</P>
Spatial stability of 3D exterior stationary Navier–Stokes flows
Elsevier 2012 Journal of mathematical analysis and applications Vol.389 No.2
<P><B>Abstract</B></P><P>In this paper, we study the stability of stationary solutions <B>w</B> for the Navier–Stokes flows in an exterior domain with zero velocity at infinity. With suitable assumptions of <B>w</B>, by the works of Chen (1993), Kozono–Ogawa (1994) and Borchers–Miyakawa (1995), if <SUB>u0</SUB>−w∈<SUP>Lr</SUP>(Ω)∩<SUP>L3</SUP>(Ω) then one can obtain‖u(t)−w<SUB>‖p</SUB>=O(<SUP>t−32(1r−1p)</SUP>)for 1<r<p<∞,‖∇(u(t)−w)<SUB>‖p</SUB>=O(<SUP>t−32(1r−1p)−12</SUP>)for 1<r<p<3, where u(x,t) is a solution of the Navier–Stokes equations with the initial condition <SUB>u0</SUB>. In this paper, we will prove that for any 0<α<3 if <SUP>|x|α</SUP>(<SUB>u0</SUB>−w) belongs to <SUP>Lr</SUP>(Ω) then one has‖<SUP>|x|α</SUP>(u(t)−w)<SUB>‖<SUP>Lp</SUP></SUB>=O(<SUP>t−32(1r−1p)+α2</SUP>)for p>3r3−rα.</P>