Logarithmic Sobolev inequalities for bounded domains and applications to drift-diffusion equations

We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel GagliardoNirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states. (c) 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).