Asymptotic behavior of solutions to the compressible Navier-Stokes equations on the half space
Asymptotic behavior of solutions to the compressible Navier-Stokes equations on the half space
复制标题
DOI：
10.4064/bc70-0-8
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Y. Kagei;Takayuki Kobayashi
中科院分区：
文献类型：
--
作者：
Y. Kagei;Takayuki Kobayashi
(0.2)m|xn=0=0，ρ(0，x)=ρ0(X)，m(0，x)=m0(X)。这里R+={x=T(x，xn)；x‘=T(x1，···，xn−1)∈R，xn>；0}，n≥2，上标T·代表换位；ρ=ρ(t，x)和m=T(m1(t，x)，.。。，Mn(t，x))分别表示在时间t≥0和位置x∈R+的未知密度和动量；P=P(ρ)是压力；ν和ν̃是满足ν>；0，2 nν+ν̃≥0的粘性系数；div m表示m在x中的通常发散；∇f表示标量函数f在x中的通常梯度。(例如，∇P(ρ)的第j个分量是∂xj P(ρ)。)符号div(m⊗mρ)表示它的第j个分量由div(mjmρ)给出。
(0.2) m|xn=0 = 0, ρ(0, x) = ρ0(x), m(0, x) = m0(x). Here R+ = {x = T ( x, xn) ; x ′ = T (x1, · · · , xn−1) ∈ R , xn > 0}, n ≥ 2, and the superscript T · stands for the transposition; ρ = ρ(t, x) and m = T (m1(t, x), . . . , mn(t, x)) denote the unknown density and momentum at time t ≥ 0 and position x ∈ R+, respectively; P = P (ρ) is the pressure; ν and ν̃ are the viscosity coefficients that satisfy ν > 0, 2 nν + ν̃ ≥ 0; div m denotes the usual divergence in x of m; and ∇f denotes the usual gradient in x of a scalar function f . (e.g., j-th component of ∇P (ρ) is ∂xj P (ρ).) The notation div ( m⊗m ρ ) means that its j-th component is given by div ( mjm ρ ).