A semigroup approach for rough partial differential equations with jumps

We establish an infinite-dimensional sewing lemma for discontinuous paths on a scale of Banach spaces. This allows us to construct Young and rough convolutions with jumps. Based on this we analyze the local and global well-posedness of semilinear parabolic rough partial differential equations (PDEs) with jumps in mixed space-time regularity spaces.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.37401
Primary Topic
Nonlinear Differential Equations Analysis
Type
preprint
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preprint

A semigroup approach for rough partial differential equations with jumps

Alexandra Blessing Neamţu, Hongjun Gao, Haoyuan Li
arXiv (Cornell University)
Nonlinear Differential Equations Analysis
preprint

A semigroup approach for rough partial differential equations with jumps

Alexandra Blessing Neamţu, Hongjun Gao, Haoyuan Li
preprint en

Abstract

We establish an infinite-dimensional sewing lemma for discontinuous paths on a scale of Banach spaces. This allows us to construct Young and rough convolutions with jumps. Based on this we analyze the local and global well-posedness of semilinear parabolic rough partial differential equations (PDEs) with jumps in mixed space-time regularity spaces.

arXiv (Cornell University)
Nonlinear Differential Equations Analysis
DOIOpen Access PDFOpenAlex
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A semigroup approach for rough partial differential equations with jumps — Alexandra Blessing Neamţu, Hongjun Gao, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS