{"publication_status":"published","title":"Upper bounds on waiting times for the Thin-film equation: The case of weak slippage","date_updated":"2021-01-12T06:49:48Z","day":"01","quality_controlled":0,"_id":"1312","page":"771 - 818","extern":1,"citation":{"apa":"Fischer, J. L. (2014). Upper bounds on waiting times for the Thin-film equation: The case of weak slippage. Archive for Rational Mechanics and Analysis. Springer. https://doi.org/10.1007/s00205-013-0690-0","ieee":"J. L. Fischer, “Upper bounds on waiting times for the Thin-film equation: The case of weak slippage,” Archive for Rational Mechanics and Analysis, vol. 211, no. 3. Springer, pp. 771–818, 2014.","ista":"Fischer JL. 2014. Upper bounds on waiting times for the Thin-film equation: The case of weak slippage. Archive for Rational Mechanics and Analysis. 211(3), 771–818.","chicago":"Fischer, Julian L. “Upper Bounds on Waiting Times for the Thin-Film Equation: The Case of Weak Slippage.” Archive for Rational Mechanics and Analysis. Springer, 2014. https://doi.org/10.1007/s00205-013-0690-0.","short":"J.L. Fischer, Archive for Rational Mechanics and Analysis 211 (2014) 771–818.","mla":"Fischer, Julian L. “Upper Bounds on Waiting Times for the Thin-Film Equation: The Case of Weak Slippage.” Archive for Rational Mechanics and Analysis, vol. 211, no. 3, Springer, 2014, pp. 771–818, doi:10.1007/s00205-013-0690-0.","ama":"Fischer JL. Upper bounds on waiting times for the Thin-film equation: The case of weak slippage. Archive for Rational Mechanics and Analysis. 2014;211(3):771-818. doi:10.1007/s00205-013-0690-0"},"year":"2014","date_published":"2014-01-01T00:00:00Z","issue":"3","status":"public","type":"journal_article","intvolume":" 211","author":[{"first_name":"Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Julian Fischer"}],"doi":"10.1007/s00205-013-0690-0","volume":211,"date_created":"2018-12-11T11:51:18Z","publication":"Archive for Rational Mechanics and Analysis","month":"01","publisher":"Springer","abstract":[{"text":"We derive upper bounds on the waiting time of solutions to the thin-film equation in the regime of weak slippage n ∈ [2, 32\\11). In particular, we give sufficient conditions on the initial data for instantaneous forward motion of the free boundary. For n ∈ (2, 32\\11), our estimates are sharp, for n = 2, they are sharp up to a logarithmic correction term. Note that the case n = 2 corresponds-with a grain of salt-to the assumption of the Navier slip condition at the fluid-solid interface. We also obtain results in the regime of strong slippage n ∈ (1,2); however, in this regime we expect them not to be optimal. Our method is based on weighted backward entropy estimates, Hardy's inequality and singular weight functions; we deduce a differential inequality which would enforce blowup of the weighted entropy if the contact line were to remain stationary for too long.","lang":"eng"}],"publist_id":"5959"}