کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10224135 | 1701078 | 2018 | 127 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The Navier-slip thin-film equation for 3D fluid films: Existence and uniqueness
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
We consider the thin-film equation âth+ââ
(h2âÎh)=0 in physical space dimensions (i.e., one dimension in time t and two lateral dimensions with h denoting the height of the film in the third spatial dimension), which corresponds to the lubrication approximation of the Navier-Stokes equations of a three-dimensional viscous thin fluid film with Navier-slip at the substrate. This equation can have a free boundary (the contact line), moving with finite speed, at which we assume a zero contact angle condition (complete-wetting regime). Previous results have focused on the 1+1-dimensional version, where it has been found that solutions are not smooth as a function of the distance to the free boundary. In particular, a well-posedness and regularity theory is more intricate than for the second-order counterpart, the porous-medium equation, or the thin-film equation with linear mobility (corresponding to Darcy dynamics in the Hele-Shaw cell). Here, we prove existence and uniqueness of classical solutions that are perturbations of an asymptotically stable traveling-wave profile. This leads to control on the free boundary and in particular its velocity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 11, 5 December 2018, Pages 5832-5958
Journal: Journal of Differential Equations - Volume 265, Issue 11, 5 December 2018, Pages 5832-5958
نویسندگان
Manuel V. Gnann, Mircea Petrache,