Large-time rescaling behaviours of Stokes and Hele-Shaw flows driven by injection. (English) Zbl 1209.35157
Summary: We give a precise description of the rescaling behaviours of global strong polynomial solutions to the reformulation of zero surface tension Hele-Shaw problem driven by injection, the Polubarinova-Galin equation, in terms of Richardson complex moments. From past results, we know that this set of solutions is large. This method can also be applied to zero surface tension Stokes flow driven by injection and a rescaling behaviour is given in terms of many conserved quantities as well.
MSC:
35R35 | Free boundary problems for PDEs |
35Q35 | PDEs in connection with fluid mechanics |
76D27 | Other free boundary flows; Hele-Shaw flows |
35C11 | Polynomial solutions to PDEs |
76M40 | Complex variables methods applied to problems in fluid mechanics |
76D45 | Capillarity (surface tension) for incompressible viscous fluids |
76D07 | Stokes and related (Oseen, etc.) flows |
Keywords:
Stokes flow; Hele-Shaw flow; Polubarinova-Galin equation; Richardson complex moments; polynomial solutionsReferences:
[1] | DOI: 10.1090/S0002-9939-04-07419-2 · Zbl 1056.30009 · doi:10.1090/S0002-9939-04-07419-2 |
[2] | DOI: 10.1007/BF02384382 · Zbl 0551.30037 · doi:10.1007/BF02384382 |
[3] | DOI: 10.1016/0898-1221(95)00044-Y · Zbl 0827.76017 · doi:10.1016/0898-1221(95)00044-Y |
[4] | DOI: 10.1017/S0022112072002551 · Zbl 0256.76024 · doi:10.1017/S0022112072002551 |
[5] | Kuznetsova, Sibirsk. Mat. Zh. 42 pp 1084– (2001) |
[6] | DOI: 10.1017/S0956792599003964 · Zbl 0955.76023 · doi:10.1017/S0956792599003964 |
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