{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:07:38Z","timestamp":1776794858257,"version":"3.51.2"},"reference-count":31,"publisher":"American Mathematical Society (AMS)","issue":"277","license":[{"start":{"date-parts":[[2012,6,28]],"date-time":"2012-06-28T00:00:00Z","timestamp":1340841600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    The goal of this paper is to present uniform-in-time error estimates by considering spectral Galerkin approximations of the Kazhikhov-Smagulov model for strong solutions. To be more precise, we derive an optimal uniform-in-time error bound in the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"bold-italic upper H Superscript 1 Baseline times upper H squared\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msup>\n                              <mml:mi mathvariant=\"bold-italic\">H<\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msup>\n                            <mml:mo>\n                              \u00d7\n                              \n                            <\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>H<\/mml:mi>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msup>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\boldsymbol {H}^1\\times H^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    norm for the velocity and density approximations being stated in Theorem 6.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2011-02491-9","type":"journal-article","created":{"date-parts":[[2011,6,28]],"date-time":"2011-06-28T15:18:19Z","timestamp":1309274299000},"page":"191-218","source":"Crossref","is-referenced-by-count":4,"title":["Uniform-in-time error estimates for spectral Galerkin approximations of a mass diffusion model"],"prefix":"10.1090","volume":"81","author":[{"given":"J.","family":"Guti\u00e9rrez-Santacreu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Rojas-Medar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2011,6,28]]},"reference":[{"issue":"5","key":"1","first-page":"171","article-title":"On the existence and regularity of the solution of Stokes problem in arbitrary dimension","volume":"67","author":"Amrouche, Ch\u00e9rif","year":"1991","journal-title":"Proc. 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