{"status":"public","author":[{"first_name":"Kyungkeun","full_name":"Kang, Kyungkeun","last_name":"Kang"},{"first_name":"Jihoon","last_name":"Lee","full_name":"Lee, Jihoon"},{"first_name":"Michael","id":"31496","full_name":"Winkler, Michael","last_name":"Winkler"}],"publication_status":"published","doi":"10.3934/dcds.2022091","abstract":[{"lang":"eng","text":"<p style='text-indent:20px;'>The Cauchy problem in <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\mathbb{R}^3 $\\end{document}</tex-math></inline-formula> for the chemotaxis-Navier–Stokes system</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> \\begin{document}$ \\begin{eqnarray*} \\left\\{ \\begin{array}{l} n_t + u\\cdot\\nabla n = \\Delta n - \\nabla \\cdot (n\\nabla c), \\\\\tc_t + u\\cdot\\nabla c = \\Delta c - nc, \\\\ \tu_t + (u\\cdot\\nabla) u = \\Delta u + \\nabla P + n\\nabla\\phi, \\qquad \\nabla \\cdot u = 0, \\ \t\\end{array} \\right. \\end{eqnarray*} $\\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is considered. Under suitable conditions on the initial data <inline-formula><tex-math id=\"M3\">\\begin{document}$ (n_0, c_0, u_0) $\\end{document}</tex-math></inline-formula>, with regard to the crucial first component requiring that <inline-formula><tex-math id=\"M4\">\\begin{document}$ n_0\\in L^1( \\mathbb{R}^3) $\\end{document}</tex-math></inline-formula> be nonnegative and such that <inline-formula><tex-math id=\"M5\">\\begin{document}$ (n_0+1)\\ln (n_0+1) \\in L^1( \\mathbb{R}^3) $\\end{document}</tex-math></inline-formula>, a globally defined weak solution with <inline-formula><tex-math id=\"M6\">\\begin{document}$ (n, c, u)|_{t = 0} = (n_0, c_0, u_0) $\\end{document}</tex-math></inline-formula> is constructed. Apart from that, assuming that moreover <inline-formula><tex-math id=\"M7\">\\begin{document}$ \\int_{ \\mathbb{R}^3} n_0(x) \\ln (1+|x|^2) dx $\\end{document}</tex-math></inline-formula> is finite, it is shown that a weak solution exists which enjoys further regularity features and preserves mass in an appropriate sense.</p>"}],"language":[{"iso":"eng"}],"intvolume":" 42","date_created":"2025-12-18T19:22:04Z","date_updated":"2025-12-18T20:08:21Z","publication_identifier":{"issn":["1078-0947","1553-5231"]},"volume":42,"type":"journal_article","_id":"63293","citation":{"mla":"Kang, Kyungkeun, et al. “Global Weak Solutions to a Chemotaxis-Navier-Stokes System in $ \\mathbb{R}^3 $.” Discrete and Continuous Dynamical Systems, vol. 42, no. 11, 5201, American Institute of Mathematical Sciences (AIMS), 2022, doi:10.3934/dcds.2022091.","ieee":"K. Kang, J. Lee, and M. Winkler, “Global weak solutions to a chemotaxis-Navier-Stokes system in $ \\mathbb{R}^3 $,” Discrete and Continuous Dynamical Systems, vol. 42, no. 11, Art. no. 5201, 2022, doi: 10.3934/dcds.2022091.","bibtex":"@article{Kang_Lee_Winkler_2022, title={Global weak solutions to a chemotaxis-Navier-Stokes system in $ \\mathbb{R}^3 $}, volume={42}, DOI={10.3934/dcds.2022091}, number={115201}, journal={Discrete and Continuous Dynamical Systems}, publisher={American Institute of Mathematical Sciences (AIMS)}, author={Kang, Kyungkeun and Lee, Jihoon and Winkler, Michael}, year={2022} }","ama":"Kang K, Lee J, Winkler M. Global weak solutions to a chemotaxis-Navier-Stokes system in $ \\mathbb{R}^3 $. Discrete and Continuous Dynamical Systems. 2022;42(11). doi:10.3934/dcds.2022091","short":"K. Kang, J. Lee, M. Winkler, Discrete and Continuous Dynamical Systems 42 (2022).","apa":"Kang, K., Lee, J., & Winkler, M. (2022). Global weak solutions to a chemotaxis-Navier-Stokes system in $ \\mathbb{R}^3 $. Discrete and Continuous Dynamical Systems, 42(11), Article 5201. https://doi.org/10.3934/dcds.2022091","chicago":"Kang, Kyungkeun, Jihoon Lee, and Michael Winkler. “Global Weak Solutions to a Chemotaxis-Navier-Stokes System in $ \\mathbb{R}^3 $.” Discrete and Continuous Dynamical Systems 42, no. 11 (2022). https://doi.org/10.3934/dcds.2022091."},"title":"Global weak solutions to a chemotaxis-Navier-Stokes system in $ \\mathbb{R}^3 $","year":"2022","issue":"11","article_number":"5201","publication":"Discrete and Continuous Dynamical Systems","publisher":"American Institute of Mathematical Sciences (AIMS)","user_id":"31496"}