{"doi":"10.1007/s00205-013-0690-0","author":[{"full_name":"Julian Fischer","first_name":"Julian L","orcid":"0000-0002-0479-558X","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"_id":"1312","title":"Upper bounds on waiting times for the Thin-film equation: The case of weak slippage","quality_controlled":0,"issue":"3","publication_status":"published","publication":"Archive for Rational Mechanics and Analysis","abstract":[{"lang":"eng","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."}],"volume":211,"date_updated":"2021-01-12T06:49:48Z","publist_id":"5959","type":"journal_article","extern":1,"intvolume":"       211","page":"771 - 818","status":"public","year":"2014","publisher":"Springer","day":"01","date_published":"2014-01-01T00:00:00Z","citation":{"chicago":"Fischer, Julian L. “Upper Bounds on Waiting Times for the Thin-Film Equation: The Case of Weak Slippage.” <i>Archive for Rational Mechanics and Analysis</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00205-013-0690-0\">https://doi.org/10.1007/s00205-013-0690-0</a>.","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.","apa":"Fischer, J. L. (2014). Upper bounds on waiting times for the Thin-film equation: The case of weak slippage. <i>Archive for Rational Mechanics and Analysis</i>. Springer. <a href=\"https://doi.org/10.1007/s00205-013-0690-0\">https://doi.org/10.1007/s00205-013-0690-0</a>","short":"J.L. Fischer, Archive for Rational Mechanics and Analysis 211 (2014) 771–818.","ama":"Fischer JL. Upper bounds on waiting times for the Thin-film equation: The case of weak slippage. <i>Archive for Rational Mechanics and Analysis</i>. 2014;211(3):771-818. doi:<a href=\"https://doi.org/10.1007/s00205-013-0690-0\">10.1007/s00205-013-0690-0</a>","mla":"Fischer, Julian L. “Upper Bounds on Waiting Times for the Thin-Film Equation: The Case of Weak Slippage.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 211, no. 3, Springer, 2014, pp. 771–818, doi:<a href=\"https://doi.org/10.1007/s00205-013-0690-0\">10.1007/s00205-013-0690-0</a>.","ieee":"J. L. Fischer, “Upper bounds on waiting times for the Thin-film equation: The case of weak slippage,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 211, no. 3. Springer, pp. 771–818, 2014."},"date_created":"2018-12-11T11:51:18Z","month":"01"}