{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:12:18Z","timestamp":1760235138775,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T00:00:00Z","timestamp":1626739200000},"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>Let U=U(t,x) for (t,x)\u2208R+\u00d7Rd and \u2202xU=\u2202xU(t,x) for (t,x)\u2208R+\u00d7R be the solution and gradient solution of the fourth order linearized Kuramoto\u2013Sivashinsky (L-KS) SPDE driven by the space-time white noise in one-to-three dimensional spaces, respectively. We use the underlying explicit kernels and symmetry analysis, yielding exact, dimension-dependent, and temporal moduli of non-differentiability for U(\u00b7,x) and \u2202xU(\u00b7,x). It has been confirmed that almost all sample paths of U(\u00b7,x) and \u2202xU(\u00b7,x), in time, are nowhere differentiable.<\/jats:p>","DOI":"10.3390\/sym13071306","type":"journal-article","created":{"date-parts":[[2021,7,20]],"date-time":"2021-07-20T11:26:10Z","timestamp":1626780370000},"page":"1306","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Temporal 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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4176-9276","authenticated-orcid":false,"given":"Changkai","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S1631-073X(03)00060-8","article-title":"A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process","volume":"336","author":"Allouba","year":"2003","journal-title":"Comptes Rendus Math. 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