Stability of singular solutions to the Navier-Stokes system. (English) Zbl 1487.35283
Summary: We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem or with the stationary problem where solutions may be singular due to singular external forces which are either singular finite measures or more general tempered distributions with bounded Fourier transforms. We present results on asymptotic properties of such solutions either for large values of the space variables (so called the far-field asymptotics) or for large values of time.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35A21 | Singularity in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35C06 | Self-similar solutions to PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35B35 | Stability in context of PDEs |
Keywords:
Navier-Stokes equation; Cauchy problem; stationary solutions; singular solutions; asymptotic behavior of solutionsReferences:
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