On the existence of finite energy weak solutions to the Navier–Stokes equations in irregular domains |
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| Authors: | Peter Kukučka |
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| Institution: | Institute of Mathematics of the Academy of Sciences of the Czech Republic, Department of Evolution Differential Equations, ?itná 25, 115 67 Praha 1, Czech Republic |
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| Abstract: | This paper studies the existence of weak solutions of the Navier–Stokes system defined on a certain class of domains in ?3 that may contain cusps. The concept of such a domain and weak energy solution for the system is defined and its existence is proved. However, thinness of cusps must be related to the adiabatic constant appearing in the pressure law. Copyright © 2008 John Wiley & Sons, Ltd. |
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| Keywords: | Navier– Stokes system renormalized solution energy inequality |
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