Fractional high order thin film equation: gradient flow approach
Stefano Lisini
TL;DR
This paper establishes the existence of weak solutions for a fractional high order thin film equation across all dimensions and orders, using a gradient flow approach in Wasserstein space.
Contribution
It introduces a novel gradient flow method to prove existence results for fractional thin film equations of any order and dimension.
Findings
Existence of weak solutions proven for fractional thin film equations.
Applicable to any space dimension and order of the equation.
Utilizes Wasserstein gradient flow techniques.
Abstract
We prove existence of weak solutions of a fractional thin film type equation in any space dimension and for any order of the equation. The proof is based on a gradient flow technique in the space of Borel probability measures endowed with the Wasserstein distance.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Fluid Dynamics and Thin Films · Navier-Stokes equation solutions