Zero-Regularity Stochastic Burgers Equations with Lévy Noise

Definitions and mathematical statement

Let $1<p\leq2$, and let $\beta\in\operatorname{Sub}(p)$ be a subordinator in the report's specified class. A subordinator is a nondecreasing Lévy process. The driving cylindrical Lévy process is written $L(t)=W(\beta(t))$, the subordinated cylindrical Wiener process in the source's construction. The Hilbert space of $W$, the subordination assumptions, and the definition of $\operatorname{Sub}(p)$ are not included in the extraction.

For the stochastic Burgers equation driven by this noise, does the stated theory and well-posedness result extend to the endpoint spatial-regularity parameter $\theta=0$, for the same stated range $1<p\leq2$ and the intended remaining assumptions? This is an endpoint question, not a request to replace cylindrical noise by a trace-class process or to impose positive spatial regularity.

The equation, spatial domain and boundary conditions, initial-data space, meaning of $\theta$, solution notion, and original well-posedness theorem are absent. Consequently one cannot specify the required existence, uniqueness, path regularity or continuous-dependence conclusions precisely, nor identify $\theta=0$ with a chosen function space, without additional source data.

Short English statement

Ask whether the report's stochastic Burgers theory for subordinated cylindrical Lévy noise extends exactly to $\theta=0$, with $\beta\in\operatorname{Sub}(p)$ and $1<p\leq2$. The noise class, equation setup and original theorem must be recovered before a complete endpoint statement is possible.

Sources

• Local UnsolvedMath registry, permanent ID $30001095$, source code catalogue entry, "Zero-Regularity Stochastic Burgers Equations with Lévy Noise." Registry curation: Ulam AI / UnsolvedMath Contributors, CC BY 4.0; underlying sources retain their supplied provenance.
• Infinite Dimensional Random Dynamical Systems and Their Applications (2009), Oberwolfach Reports, pp. 2815--2874, DOI https://doi.org/10.4171/owr/2008/50.
• Supplied "Brzeźniak--Zabczyk, Levy white noise and Burgers": https://arxiv.org/abs/0901.0028.
• Supplied literature triage, literature_checked_at: 2026-08-21: labeled open; says the $\theta=0$ case for the specified cylindrical Lévy noise was explicitly left open, while later nearby Gaussian, trace-class or positive-regularity results do not resolve this endpoint. This is supplied dated curation, not independently verified.