| 실적년도 | 2014년 |
|---|---|
| 논문구분 | 국외 |
| 총저자 | Dongho Chae |
| 학술지명 | Advances in Mathematics |
| 권(Vol.) | 254 |
| 호(No.) | |
| 게재년월 | 2014년 3월 |
| Impact Factor | |
| SCI 등재 | SCI |
| 비고 |
Let (v,p) be a smooth solution pair of the velocity and the pressure for the
Navier-Stokes (Euler) equations on RN × (0,T), N ≥ 3. We set the
Bernoulli function Q=1/2|v|2+p. Under suitable decay conditions at
infinity for (v,p) we prove that for almost all α(t) and β(t) defined on (0, T)
there holds, where ω=curlv is the vorticity. This shows that, in each region
squeezed between two levels of the Bernoulli function, besides the energy
dissipation due to the enstrophy, the energy flows into the region through the
level hypersurface having the higher level, and the energy flows out of the
region through the level hypersurface with the lower level. Passing
α(t)↓infx∈RNQ(x,t) and β(t)↑supx∈RNQ(x,t), we recover the
well-known energy equality, 1/2 d/dt
∫RN|v|2=-ν∫RN|ω|2dx. A weaker
version of the above equality under the weaker decay assumption of the solution
at spatial infinity is also derived. The stationary version of the equality
implies the previous Liouville type results on the Navier-Stokes equations.
