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Global existence and exponential decay of strong solutions for the inhomogeneous incompressible Navier-Stokes equations with vacuum (1806.04464v1)
Published 12 Jun 2018 in math.AP
Abstract: The inhomogeneous incompressible Navier-Stokes equations with fractional Laplacian dissipations in the multi-dimensional whole space are considered. The existence and uniqueness of global strong solution with vacuum are established for large initial data. The exponential decay-in-time of the strong solution is also obtained, which is different from the homogeneous case. The initial density may have vacuum and even compact support.