Existence of a weak solution to the Navier–Stokes equation in a general time‐varying domain by the Rothe method |
| |
Authors: | Jiří Neustupa |
| |
Institution: | Czech Academy of Sciences, Mathematical Institute, ?itná 25, 115 67 Praha 1, Czech Republic |
| |
Abstract: | We assume that Ωt is a domain in ?3, arbitrarily (but continuously) varying for 0?t?T. We impose no conditions on smoothness or shape of Ωt. We prove the global in time existence of a weak solution of the Navier–Stokes equation with Dirichlet's homogeneous or inhomogeneous boundary condition in Q0, T) := {( x , t);0?t?T, x ∈Ωt}. The solution satisfies the energy‐type inequality and is weakly continuous in dependence of time in a certain sense. As particular examples, we consider flows around rotating bodies and around a body striking a rigid wall. Copyright © 2008 John Wiley & Sons, Ltd. |
| |
Keywords: | Navier– Stokes equations weak solutions |
|
|