Article Contents
Article Contents

$L^p$-theory for the Navier-Stokes equations with pressure boundary conditions

• We consider the Navier-Stokes equations with pressure boundary conditions in the case of a bounded open set, connected of class $\mathcal{C}^{\,1,1}$ of $\mathbb{R}^3$. We prove existence of solution by using a fixed point theorem over the type-Oseen problem. This result was studied in [5] in the Hilbertian case. In our study we give the $L^p$-theory for $1< p <\infty$.
Mathematics Subject Classification: Primary: 35J25, 35J47, 35J50, 35J57; Secondary: 76D05, 76D07.

 Citation:

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