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The existence and space-time decay rates of strong solutions Navier-Stokes Equations in weighed L^\infty(|x|^\gamma{\rm dx})\cap L^\infty(|x|^\beta{\rm dx}) spaces
  • Khai Dao
Khai Dao
Institute of Mathematics, Vietnam Academy of Science and Technology

Corresponding Author:[email protected]

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Abstract

In this paper, we prove some results on the existence and space-time decay properties of higher order derivatives in time and space variables of global strong solutions of the Cauchy problem for the Navier-Stokes equations in weighed L^\infty(\mathbb R^d,|x|^\gamma{\rm dx})\cap L^\infty(\mathbb R^d,|x|^\beta{\rm dx}) spaces. The estimate for the decay rate is optimal in the sense that it coincides with the decay rate of a solution to the heat equation.