The authors study radial solutions to a model equation for the Navier-Stokes equations. It is shown that the model equation has self-similar singular solution if 5 ≤ n ≤ 9. It is also shown that the solution will blow up if the initial data is radial, large enough and n ≥ 5.
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Project supported by the China Postdoctoral Science Foundation (No. 20070410683).
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Du, D., Lü, J. Blow-up for a semi-linear advection-diffusion system with energy conservation. Chin. Ann. Math. Ser. B 30, 433–446 (2009). https://doi.org/10.1007/s11401-007-0474-7
- Navier-Stokes equations
- Self-similar singular solutions
2000 MR Subject Classification