Work

On well-posedness for parabolic Cauchy problems of Lions type with rough initial data

Year: 2025

Type: article

Abstract: We establish a complete picture for well-posedness of parabolic Cauchy problems with time-independent, uniformly elliptic, bounded measurable complex coefficients. We exhibit a range of p for which tempered distributions in homogeneous Hardy–Sobolev spaces $$\dot{H}^{s,p}$$ H ˙ s , p with regularity index $$s \in (-1,1)$$ s ∈ ( - 1 , 1 ) are initial data. Source terms of Lions’ type lie in weighted tent spaces, and weak solutions are built with their gradients in weighted tent spaces as well. A similar result can be achieved for initial data in homogeneous Besov spaces $$\dot{B}^{s}_{p,p}$$ B ˙ p , p s .

Source: Mathematische Annalen

DOI: 10.1007/s00208-025-03149-y

Authors: Pascal Auscher, Hedong Hou

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Université Paris-Saclay