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Within a purely interior framework, Constantin and Vicol showed that the two-dimensional viscosity limit is justified for any arbitrary but finite time under the assumption that on each compactly contained subset of the domain, the enstrophies are bounded uniformly along the viscosity sequence. Within this framework, we upgrade to local strong convergence of the vorticities under a similar assumption on the\n                    <jats:italic>p<\/jats:italic>\n                    -enstrophies,\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$p&gt;2$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . The key novel idea is the analysis of the evolution of the weak convergence defect.\n                  <\/jats:p>","DOI":"10.1007\/s00332-026-10239-x","type":"journal-article","created":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T03:47:20Z","timestamp":1769226440000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Strong Convergence of Vorticities in the 2D Viscosity Limit on a Bounded Domain"],"prefix":"10.1007","volume":"36","author":[{"given":"Christian","family":"Seis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emil","family":"Wiedemann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakub","family":"Wo\u017anicki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,24]]},"reference":[{"issue":"1","key":"10239_CR1","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/s40818-019-0066-3","volume":"5","author":"Giovanni Alberti","year":"2019","unstructured":"Alberti, Giovanni, Crippa, Gianluca, Mazzucato, Anna L.: Loss of regularity for the continuity equation with non-Lipschitz velocity field. 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