In this paper, we provide a much simplified proof of the main result in Lin and Zhang (Commun Pure Appl Math 67: 531–580, 2014) concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a three dimensional incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Besides the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the L∞ estimates for time slices to deduce the key L1 in time estimates. The latter is responsible for the global in time existence.
|Original language||English (US)|
|Number of pages||16|
|Journal||Archive for Rational Mechanics and Analysis|
|State||Published - Jun 1 2015|
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Mechanical Engineering