Spreading equilibria under mildly singular potentials: pancakes versus droplets
From MaRDI portal
Publication:2168676
DOI10.1007/s00332-022-09826-5zbMath1503.35158arXiv2109.06683OpenAlexW3201645118MaRDI QIDQ2168676
Riccardo Durastanti, Lorenzo Giacomelli
Publication date: 26 August 2022
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.06683
asymptotic behavioruniquenessfree boundary problemslubrication theoryscaling lawprecursordropletsingular potentialthin-film equationmass constraintpartial wettingcomplete wettingsingular minimization problemattractive-repulsive potentialAlt-Caffarelli functionalAlt-Phillips functionaleffective contact angleinter-molecular potentialmacroscopic contact anglepancakespreading coefficient
PDEs in connection with fluid mechanics (35Q35) Thin fluid films (76A20) Lubrication theory (76D08) Existence theories for free problems in two or more independent variables (49J10) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35) Qualitative investigation and simulation of ordinary differential equation models (34C60) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Existence theories for free problems in one independent variable (49J05) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Related Items (4)
Thin-film equations with singular potentials: an alternative solution to the contact-line paradox ⋮ A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems ⋮ Elliptic regularization of some semilinear parabolic free boundary problems ⋮ The Dirichlet problem for possibly singular elliptic equations with degenerate coercivity
Cites Work
- Behaviour of free boundaries in thin-film flow: the regime of strong slippage and the regime of very weak slippage
- On the regularity for the Navier-slip thin-film equation in the perfect wetting regime
- Darcy's flow with prescribed contact angle: well-posedness and lubrication approximation
- Well-posedness for a class of thin-film equations with general mobility in the regime of partial wetting
- The thin film equation with backwards second order diffusion
- Energy minimizers of a thin film equation with Born repulsion force
- Higher order nonlinear degenerate parabolic equations
- Smooth zero-contact-angle solutions to a thin-film equation around the steady state
- The theory of differential equations. Classical and qualitative
- Multiplicity of positive solutions for a singular and critical problem
- Rigorous lubrication approximation
- Linear stability of steady states for thin film and Cahn-Hilliard type equations
- Elliptic partial differential equations of second order
- Energy levels of steady states for thin-film-type equations
- Existence of nonnegative solutions to singular elliptic problems, a variational approach
- Energy stability of droplets and dry spots in a thin film model of hanging drops
- The thin-film equation close to self-similarity
- The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness
- Convex rearrangement: Equality cases in the Pólya-Szegö inequality
- Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation
- Degenerate parabolic differential equations of fourth order and a plasticity model with nonlocal hardening
- Finite speed of propagation and continuity of the interface for thin viscous flows
- Well-posedness and uniform bounds for a nonlocal third order evolution operator on an infinite wedge
- The thin viscous flow equation in higher space dimensions
- Nonlinear dynamics of dewetting thin films
- Comparison principle for elliptic equations with mixed singular nonlinearities
- Boundary spike of the singular limit of an energy minimizing problem
- Weak solutions to thin-film equations with contact-line friction
- Finite and infinite energy solutions of singular elliptic problems: existence and uniqueness
- Singular limit of an energy minimizer arising from dewetting thin film model with Van der waal, born repulsion and surface tension forces
- Scaling laws for droplets spreading under contact-line friction
- The role of the power 3 for elliptic equations with negative exponents
- Well-posedness for the Navier-slip thin-film equation in the case of complete wetting
- Upper bounds on waiting times for the thin-film equation: the case of weak slippage
- Lower bounds on waiting times for degenerate parabolic equations and systems
- Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
- Surface-tension-driven dewetting of Newtonian and power-law fluids
- Thin-film equations with ``partial wetting energy: Existence of weak solutions
- Semilinear problems with right-hand sides singular at \(u=0\) which change sign
- Simulation of singularities and instabilities arising in thin film flow
- Droplet profiles under the influence of van der Waals forces
- Dewetting films: bifurcations and concentrations
- THE THIN FILM EQUATION WITH NONLINEAR DIFFUSION
- Dynamics and equilibria of thin viscous coating films on a rotating sphere
- Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner’s law
- Convergence to Equilibrium for a Thin-Film Equation on a Cylindrical Surface
- Sets of Finite Perimeter and Geometric Variational Problems
- On the stability of single and multiple droplets for equations of thin film type
- On a Singular Nonlinear Elliptic Boundary-Value Problem
- Coarsening Rates for a Droplet Model: Rigorous Upper Bounds
- The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow
- On a Minimization Problem Arising in Wetting
- Rival contact-angle models and the spreading of drops
- On a dirichlet problem with a singular nonlinearity
- Lubrication approximation with prescribed nonzero contact anggle
- A singular minimization problem for droplet profiles
- The lubrication approximation for thin viscous films: the moving contact line with a 'porous media' cut-off of van der Waals interactions
- On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
- Effective and microscopic contact angles in thin film dynamics
- Liquid Drops on a Rough Surface
- Stability and instability of axisymmetric droplets in thermocapillary-driven thin films
- Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle
- Droplet Spreading Under Weak Slippage—Existence for the Cauchy Problem
- Properties of steady states for thin film equations
- THE SPREADING OF A THIN DROP BY GRAVITY AND CAPILLARITY
- On the motion of a fluid-fluid interface along a solid surface
- Droplet spreading: Intermediate scaling law by PDE methods
- Shear-thinning liquid films: macroscopic and asymptotic behaviour by quasi-self-similar solutions
- Moving Contact Lines: Scales, Regimes, and Dynamical Transitions
- A mountain pass scenario and heteroclinic orbits for thin-film type equations
- On the Relationship Between the Thin Film Equation and Tanner's Law
- Well‐posedness for the Navier Slip Thin‐Film equation in the case of partial wetting
- Continuum models for the contact line problem
- The Thin Film Equation with Non-Zero Contact Angle: A Singular Perturbation Approach
- On steady states of van der Waals force driven thin film equations
- Well-Posedness and Self-Similar Asymptotics for a Thin-Film Equation
- Ostwald ripening of droplets: The role of migration
- The effect of the contact line on droplet spreading
- Positive solutions for singular nonlinear elliptic equations
- Steady states of thin film droplets on chemically heterogeneous substrates
- Variational formulation for the lubrication approximation of the Hele-Shaw flow
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Spreading equilibria under mildly singular potentials: pancakes versus droplets
