{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:10:29Z","timestamp":1760235029906,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,12]],"date-time":"2021-07-12T00:00:00Z","timestamp":1626048000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto\u2013Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao\u2019s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.<\/jats:p>","DOI":"10.3390\/sym13071251","type":"journal-article","created":{"date-parts":[[2021,7,12]],"date-time":"2021-07-12T21:56:52Z","timestamp":1626127012000},"page":"1251","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Spatial Moduli of Non-Differentiability for Linearized Kuramoto\u2013Sivashinsky SPDEs and Their Gradient"],"prefix":"10.3390","volume":"13","author":[{"given":"Wensheng","family":"Wang","sequence":"first","affiliation":[{"name":"School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6851","DOI":"10.1016\/j.jde.2015.08.033","article-title":"L-Kuramoto-Sivashinsky SPDEs in one-to-three dimensions: L-KS kernel, sharp H\u00f6lder regularity, and Swift-Hohenberg law equivalence","volume":"259","author":"Allouba","year":"2015","journal-title":"J. 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