The Navier-Stokes equations and weak Herz spaces

By Yohei Tsutsui. Advances in Differential Equations, 2011

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In this paper, we discuss the Cauchy problem for Navier-Stokes equations in homogeneous weak Herz spaces WK̇ p,q(R). More precisely, we construct the solution in the class L∞(0, T ; WK̇ p,q) with the initial data in WK̇ α p,q. Further, we consider the blow-up phenomena of time-local solutions and the uniqueness of global solutions with large initial data in WK̇ p,q. Also, we give several embeddings of weak Herz spaces into homogeneous Besov spaces Ḃ−α p,∞(R), (α > 0), or bmo−1(Rn).

Subfields: Applied Mathematics, Mathematical Physics

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