Article ID Journal Published Year Pages File Type
4615702 Journal of Mathematical Analysis and Applications 2014 38 Pages PDF
Abstract

In this paper, we construct local solution with highly oscillating initial velocity and then get the global strong solution in the LpLp based Besov space which improves the result of J. Qian, Z. Zhang (2010) [25] and X. Hu, D. Wang (2011) [14]. The local existence and uniqueness lies on the Lagrange coordinate transform and the contraction mapping theorem. The global result lies on a decomposition of the system and some commutator estimates. In the last part, we prove a time-decay in the critical Besov space framework which seems to have little investigation. The proof is based on the properties of the Green's matrix and various interpolations between Besov type spaces.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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