Classical solutions to Navier–Stokes equations for nonhomogeneous incompressible fluids with non-negative densities |
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| Authors: | Tong Lining Yuan Hongjun |
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| Affiliation: | aDepartment of Mathematics, Shanghai University, Shanghai 200444, China;bInstitute of Mathematics, Jilin University, Changchun, Jilin 130012, China |
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| Abstract: | We study the Navier–Stokes equations for nonhomogeneous incompressible fluids in a bounded domain Ω of R3. We first prove the existence and uniqueness of local classical solutions to the initial boundary value problem of linear Stokes equations and then we obtain the existence and uniqueness of local classical solutions to the Navier–Stokes equations with vacuum under the assumption that the data satisfies a natural compatibility condition. |
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| Keywords: | Navier– Stokes equations Incompressible fluids Classical solutions |
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