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Well-posedness and decay for the dissipative system modeling electro-hydrodynamics in negative Besov spaces.
- Source :
-
Journal of Differential Equations . Jul2017, Vol. 263 Issue 2, p1293-1322. 30p. - Publication Year :
- 2017
-
Abstract
- In Guo and Wang (2012) [10] , Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier–Stokes equations and the Poisson–Nernst–Planck equations through charge transport and external forcing terms. We show that some weighted negative Besov norms of solutions are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 263
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 122370511
- Full Text :
- https://doi.org/10.1016/j.jde.2017.03.015