{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:42:51Z","timestamp":1776840171142,"version":"3.51.2"},"reference-count":32,"publisher":"American Mathematical Society (AMS)","issue":"355","license":[{"start":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:00:00Z","timestamp":1761609600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100014717","name":"National Outstanding Youth Science Fund Project of National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201342"],"award-info":[{"award-number":["12201342"]}],"id":[{"id":"10.13039\/100014717","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014717","name":"National Outstanding Youth Science Fund Project of National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201342"],"award-info":[{"award-number":["12201342"]}],"id":[{"id":"10.13039\/100014717","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014717","name":"National Outstanding Youth Science Fund Project of National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201342"],"award-info":[{"award-number":["12201342"]}],"id":[{"id":"10.13039\/100014717","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014717","name":"National Outstanding Youth Science Fund Project of National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12201342"],"award-info":[{"award-number":["12201342"]}],"id":[{"id":"10.13039\/100014717","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We investigate a filtered Lie-Trotter splitting scheme for the \u201cgood\u201d Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use of discrete Bourgain spaces, our analysis extends to initial data in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript s\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>s<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^{s}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"0 greater-than s less-than-or-equal-to 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mn>0<\/mml:mn>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">0&gt;s\\leq 2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , overcoming the constraint of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"s greater-than 1 slash 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>s<\/mml:mi>\n                            <mml:mo>&gt;<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">s&gt;1\/2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"tau Superscript s slash 2\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>\n                              \u03c4\n                              \n                            <\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi>s<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mo>\/<\/mml:mo>\n                              <\/mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\tau ^{s\/2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for such levels of regularity. Our analytical findings are supported by numerical experiments.\n                  <\/p>","DOI":"10.1090\/mcom\/4023","type":"journal-article","created":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T17:32:18Z","timestamp":1730136738000},"page":"2345-2365","source":"Crossref","is-referenced-by-count":0,"title":["Filtered Lie-Trotter splitting for the \u201cgood\u201d Boussinesq equation: Low regularity error estimates"],"prefix":"10.1090","volume":"94","author":[{"given":"Lun","family":"Ji","sequence":"first","affiliation":[]},{"given":"Hang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Alexander","family":"Ostermann","sequence":"additional","affiliation":[]},{"given":"Chunmei","family":"Su","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,10,28]]},"reference":[{"key":"1","first-page":"55","article-title":"Th\u00e9orie des ondes et des remous qui se propagent le long d\u2019un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond","volume":"17","author":"Boussinesq, J.","year":"1872","journal-title":"J. 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