Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

Details Global exponential stability of classical solutions to the hydrodynamic model for semiconductors Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

2007-03-22

arxiv.org/abs/math/0703659v1

Math. Models Methods Appl. Sci. 17(2007) 1507-1530

Mathematics

Analysis of PDEs

18 pages

Scientific paper

10.1142/S0218202507002364

In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve some known results in Sobolev space. The local existence of classical solutions to the Cauchy problem is obtained by the regularized means and compactness argument. Using the high- and low- frequency decomposition method, we prove the global exponential stability of classical solutions (close to equilibrium). Furthermore, it is also shown that the vorticity decays to zero exponentially in the 2D and 3D space. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.

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