l******n 发帖数: 9344 | 1 一个distribution function defined as:
phi: [0,T]*Omega*S^2 ----> Omega
Omega is a domain in R^n.(you can take n=3)
phi satisfies the following equation
dphi/dt + (v*\nabla)phi=\Delta phi + \nabla \cdot (g*phi)
v is H^1 in Omega, the first \nabla is direvatives to variables in Omega
, the second \nabla is direvatves to variables in S^2, g is a smooth fun
ction on S^2.
initially phi is smooth, has anybody any idea how to prove that phi is H
^1(Omega) or L^2(Omega)?
Or if you know any papers related, |
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