Study on half-space problem for non-linear PDE in Fluid Dynamics and its application

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In this study, we studied analysis of weighted Lp space of Navier-Stokes equation, which is the basic equation of fluid dynamics. As a result, if the weight function belongs to the Muckenhoupt weight class, we are able to prove the weighted Lp-Lq estimates of Stokes semigroup in exterior domains, half-spaces and perturbed half spaces. Moreover we could also show the unique existence of the solution to the Navier-Stokes equations and its asymptotic behavior in weighted Lp framework.