{"id":2,"date":"2022-09-22T23:49:24","date_gmt":"2022-09-22T23:49:24","guid":{"rendered":"https:\/\/blogs.oregonstate.edu\/tpham\/?page_id=2"},"modified":"2025-09-18T01:40:13","modified_gmt":"2025-09-18T11:40:13","slug":"projects","status":"publish","type":"page","link":"https:\/\/blogs.oregonstate.edu\/tpham\/projects\/","title":{"rendered":"Projects"},"content":{"rendered":"\n<p>My research fields are Partial Differential Equations, Probability, Fluid Dynamics, and Numerical Analysis. I investigate differential equations from analytic, probabilistic, and numerical perspectives. <em>If you are interested to be involved in a project, either at an undergraduate or graduate level, please feel free to contact me.<\/em><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>My current projects are on:<\/strong>\n<ol class=\"wp-block-list\">\n<li>the regularity of the Navier-Stokes equations,<\/li>\n\n\n\n<li>the symbiotic relations between the Navier-Stokes equations (or related differential equations such as the <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Calpha&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\alpha' title='\\alpha' class='latex' \/>-Riccati equation, the Burgers equation, the KPP equation, the Montgomery-Smith equation) and the associated stochastic cascades,<\/li>\n\n\n\n<li>singularities of the complex Burgers equation,<\/li>\n\n\n\n<li>numerical simulations and Monte Carlo simulations for fluid flows,<\/li>\n\n\n\n<li>hydrodynamic stability of plane Couette flow and Rayleigh-B\u00e9nard convection.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Presentations\/seminars.html\">Seminar lectures<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Gallery.htm\" data-type=\"link\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Gallery.htm\">Gallery<\/a><\/li>\n\n\n\n<li>Instructions for BYUH Research Assistants:\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Resource\/Workspace-setup-simplified.pdf\" data-type=\"link\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Resource\/Workspace-setup-simplified.pdf\">Set up workspace<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Resource\/Inkscape-related\/Inkscape-With-LaTeX.pdf\" data-type=\"link\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Resource\/Inkscape-related\/Inkscape-With-LaTeX.pdf\">Install Inkscape with LaTeX extension<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Resource\/Mathematica-related\/Wolfram-Mathematica-With-JupyterLab.pdf\" data-type=\"link\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Resource\/Mathematica-related\/Wolfram-Mathematica-With-JupyterLab.pdf\">Integrate Wolfram Language into JupyterLab<\/a><\/li>\n<\/ol>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Publications:<\/strong>\n<ol class=\"wp-block-list\">\n<li>Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: &#8220;Navier-Stokes Equations with Fractional Dissipation and Associated Doubly Stochastic Yule Cascades&#8221; (available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2509.10806\" data-type=\"link\" data-id=\"https:\/\/arxiv.org\/abs\/2509.10806\">arXiv:2509.10806<\/a>).<\/li>\n\n\n\n<li>Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: &#8220;Transformation of Stochastic Recursions and Critical Phenomena in the Analysis of the Aldous-Shields-Athreya Cascade and Related Mean Flow Equations&#8221; (submitted, available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2411.00629\" data-type=\"link\" data-id=\"https:\/\/arxiv.org\/abs\/2411.00629\">arXiv:2411.00629<\/a>).<\/li>\n\n\n\n<li>Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: &#8220;Erratum to Stochastic explosion and non-uniqueness for&nbsp;<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Calpha&#038;bg=ffffff&#038;fg=000000&#038;s=0' alt='\\alpha' title='\\alpha' class='latex' \/>-Riccati equation&#8221;. <em>Journal of Mathematical Analysis and Applications, Vol 527, Issue 2.<\/em> (Also available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2303.05482\" data-type=\"URL\" data-id=\"https:\/\/arxiv.org\/abs\/2303.05482\">arXiv:2103.06912<\/a>).<\/li>\n\n\n\n<li>Radu Dascaliuc, Tuan Pham and Enrique Thomann: &#8220;On Le Jan-Sznitman&#8217;s stochastic approach to the Navier-Stokes equations&#8221;. <em>Transactions of the American Mathematical Society, Vol 377, No. 4, 2335-2365, April 2024.<\/em> (Also available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1910.05500\">arXiv:1910.05500<\/a>).<\/li>\n\n\n\n<li>Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: &#8220;Doubly Stochastic Yule Cascades (Part I): The explosion problem in the time-reversible case&#8221;. <em>Journal of Functional Analysis, Vol 284, Issue 1, 2023.<\/em> (Also available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2103.06912\">arXiv:2103.06912<\/a>).<\/li>\n\n\n\n<li>Radu Dascaliuc, Tuan Pham, Enrique Thomann, and Edward Waymire: &#8220;Doubly Stochastic Yule Cascades (Part II): The explosion problem in the non-reversible case&#8221;. <em><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Stochastic-cascade-Part-II.pdf\" data-type=\"URL\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Stochastic-cascade-Part-II.pdf\">Annales de l&#8217;Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques, No. 4, Vol 59, 1904-1933, 2023.<\/a><\/em> (Also available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/2107.13182\">arXiv:2107.13182<\/a>).<\/li>\n\n\n\n<li>Tuan Pham: &#8220;Global regularity criteria for the Navier-Stokes equations based on one approximate solution&#8221; (submitted, available online at&nbsp;<a href=\"https:\/\/arxiv.org\/abs\/1910.05501\">arXiv:1910.05501).<\/a><\/li>\n\n\n\n<li>Tuan Pham and Jared Whitehead: &#8220;Hydrodynamic stability in the presence of stochastic forcing&#8221; (in preparation)<\/li>\n\n\n\n<li>Tuan Pham and Vladimir Sverak: &#8220;Minimal blow-up data for potential Navier-Stokes singularities in the half space&#8221; (in preparation).<\/li>\n\n\n\n<li>Tuan Pham: &#8220;On the explosion problem of nonhomogeneous Yule cascades&#8221; (in preparation).<\/li>\n\n\n\n<li>Tuan Pham: &#8220;Conservation of frequencies and the global regularity of the Navier-Stokes equations&#8221; (in preparation).<\/li>\n\n\n\n<li>Tuan Pham: &#8220;Topics on the regularity theory of the Navier-Stokes equations&#8221;&nbsp;<a href=\"http:\/\/hdl.handle.net\/11299\/201125\">PhD thesis<\/a>&nbsp;2018.<\/li>\n\n\n\n<li>D. Nguyen, T. Pham and Q. Phan, &#8220;A Semantic Model for Building the Vietnamese Language Query Processing Framework in e-Library Searching Application,&#8221; in 2nd International Conference on Machine Learning and Computing, Bangalore, 2010 pp. 179-183. <a href=\"https:\/\/dl.acm.org\/doi\/abs\/10.1109\/ICMLC.2010.17\">doi:10.1109\/ICMLC.2010.17<\/a><\/li>\n<\/ol>\n<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Other research works:<\/strong>\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Complex-Burgers-singularities.pdf\" data-type=\"link\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Complex-Burgers-singularities.pdf\">Complex Burgers singularities<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Linear-PDE-constant-coefficients.pdf\" data-type=\"link\" data-id=\"https:\/\/web.engr.oregonstate.edu\/~phamt3\/Projects\/Linear-PDE-constant-coefficients.pdf\">Linear PDE with constant coefficients<\/a><\/li>\n<\/ol>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-right\"><sub>Last updated: Sep 18, 2025<\/sub><\/p>\n","protected":false},"excerpt":{"rendered":"<p>My research fields are Partial Differential Equations, Probability, Fluid Dynamics, and Numerical Analysis. I investigate differential equations from analytic, probabilistic, and numerical perspectives. If you are interested to be involved in a project, either at an undergraduate or graduate level, &hellip; <a href=\"https:\/\/blogs.oregonstate.edu\/tpham\/projects\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":12738,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-2","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/pages\/2","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/users\/12738"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/comments?post=2"}],"version-history":[{"count":51,"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/pages\/2\/revisions"}],"predecessor-version":[{"id":1507,"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/pages\/2\/revisions\/1507"}],"wp:attachment":[{"href":"https:\/\/blogs.oregonstate.edu\/tpham\/wp-json\/wp\/v2\/media?parent=2"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}