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# Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition

• In this paper, we study the existence and regularity of solutions to the Stokes and Oseen equations with a nonhomogeneous divergence condition. We also prove the existence of global weak solutions to the 3D Navier-Stokes equations when the divergence is not equal to zero. These equations intervene in control problems for the Navier-Stokes equations and in fluid-structure interaction problems.
Mathematics Subject Classification: Primary: 35Q30, 76D05, 76D03; Secondary: 76D07.

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