On Hausdorff Dimension of Blow-Up Times Relevant to Weak Solution of Generalized Navier-Stokes Fluids
| Type of publication: | Inbook |
| Citation: | |
| Booktitle: | Mathematical Analysis on the Navier-Stokes Equations and Related Topics, Past and Future In memory of Professor Tetsuro Miyakawa |
| Series: | Mathematical Sciences and Applications |
| Volume: | 35 |
| Year: | 2011 |
| Pages: | 116--129 |
| Publisher: | Gakuto International Series |
| Note: | Preprint NCMM no. 2010-032 |
| URL: | http://www.karlin.mff.cuni.cz/... |
| Abstract: | We consider an initial and spatially periodic problem for °ows of generalized Navier-Stokes °uids (of power-law type). We study qualitative properties of weak solutions, which are known to exist for large-data and on an arbitrary time interval, in the case where the weak solution itself is not an admissible test function in the balance of linear momentum. We focus on establishing the upper estimates of the Hausdor® dimension of the possible times at which the singularity can occur - the L2 -norm of the velocity gradient can blow up. We provide a simple method that improves the estimates known before in two ways: the estimates are valid for larger range of model parameters and the estimates are sharper. For some values of model parameters, we establish new results concerning uniqueness of the strong solution in the class of weak solutions satisfying the energy inequality. |
| Keywords: | Generalized Navier-Stokes fluid, Hausdorf measure, Power-law fluid, singular set, times of blow-up, weak solution |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
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