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The main result states that the influence of the body on the fluid is negligible if (i) the diameter of the body is small and (ii) the fluid is nearly incompressible (the low Mach number regime). The specific shape of the body as well as the boundary conditions on the fluid\u2013body interface are irrelevant and collisions with the boundary <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\partial \\Omega $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>\u2202<\/mml:mi>\n                    <mml:mi>\u03a9<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are allowed. The rigid body motion may be enforced externally or governed solely by its interaction with the fluid.<\/jats:p>","DOI":"10.1007\/s00332-023-09949-3","type":"journal-article","created":{"date-parts":[[2023,8,8]],"date-time":"2023-08-08T09:02:13Z","timestamp":1691485333000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Motion of a Nearly Incompressible Viscous Fluid Containing a Small Rigid Body"],"prefix":"10.1007","volume":"33","author":[{"given":"Eduard","family":"Feireisl","sequence":"first","affiliation":[]},{"given":"Arnab","family":"Roy","sequence":"additional","affiliation":[]},{"given":"Arghir","family":"Zarnescu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,8]]},"reference":[{"issue":"3","key":"9949_CR1","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1007\/s10231-019-00917-x","volume":"199","author":"A Abbatiello","year":"2020","unstructured":"Abbatiello, A., Feireisl, E.: On a class of generalized solutions to equations describing incompressible viscous fluids. 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