{"intvolume":" 26","date_created":"2025-12-18T19:05:09Z","date_updated":"2025-12-18T20:13:58Z","type":"journal_article","publication_identifier":{"issn":["1422-6928","1422-6952"]},"volume":26,"author":[{"full_name":"Fuest, Mario","last_name":"Fuest","first_name":"Mario"},{"id":"31496","first_name":"Michael","full_name":"Winkler, Michael","last_name":"Winkler"}],"status":"public","abstract":[{"lang":"eng","text":"AbstractThe chemotaxis-Navier–Stokes system $$\\begin{aligned} \\left\\{ \\begin{array}{rcl} n_t+u\\cdot \\nabla n & =& \\Delta \\big (n c^{-\\alpha } \\big ), \\\\ c_t+ u\\cdot \\nabla c & =& \\Delta c -nc,\\\\ u_t + (u\\cdot \\nabla ) u & =& \\Delta u+\\nabla P + n\\nabla \\Phi , \\qquad \\nabla \\cdot u=0, \\end{array} \\right. \\end{aligned}$$\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n n\r\n t\r\n \r\n +\r\n u\r\n ·\r\n ∇\r\n n\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n \r\n (\r\n \r\n n\r\n \r\n c\r\n \r\n -\r\n α\r\n \r\n \r\n \r\n )\r\n \r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n c\r\n t\r\n \r\n +\r\n u\r\n ·\r\n ∇\r\n c\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n c\r\n -\r\n n\r\n c\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n u\r\n t\r\n \r\n +\r\n \r\n (\r\n u\r\n ·\r\n ∇\r\n )\r\n \r\n u\r\n \r\n \r\n \r\n =\r\n \r\n \r\n \r\n Δ\r\n u\r\n +\r\n ∇\r\n P\r\n +\r\n n\r\n ∇\r\n Φ\r\n ,\r\n \r\n ∇\r\n ·\r\n u\r\n =\r\n 0\r\n ,\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain $$\\Omega \\subset \\mathbb R^2$$\r\n \r\n Ω\r\n ⊂\r\n \r\n R\r\n 2\r\n \r\n \r\n . For all $$\\alpha > 0$$\r\n \r\n α\r\n >\r\n 0\r\n \r\n and all sufficiently regular $$\\Phi $$\r\n Φ\r\n , we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time $$L^p$$\r\n \r\n L\r\n p\r\n \r\n estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time $$L^2$$\r\n \r\n L\r\n 2\r\n \r\n norm of the force term raised to an arbitrary small power."}],"language":[{"iso":"eng"}],"doi":"10.1007/s00021-024-00899-8","publication_status":"published","article_number":"60","issue":"4","user_id":"31496","publication":"Journal of Mathematical Fluid Mechanics","publisher":"Springer Science and Business Media LLC","title":"Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing","citation":{"ama":"Fuest M, Winkler M. Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. Journal of Mathematical Fluid Mechanics. 2024;26(4). doi:10.1007/s00021-024-00899-8","chicago":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” Journal of Mathematical Fluid Mechanics 26, no. 4 (2024). https://doi.org/10.1007/s00021-024-00899-8.","apa":"Fuest, M., & Winkler, M. (2024). Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing. Journal of Mathematical Fluid Mechanics, 26(4), Article 60. https://doi.org/10.1007/s00021-024-00899-8","short":"M. Fuest, M. Winkler, Journal of Mathematical Fluid Mechanics 26 (2024).","bibtex":"@article{Fuest_Winkler_2024, title={Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing}, volume={26}, DOI={10.1007/s00021-024-00899-8}, number={460}, journal={Journal of Mathematical Fluid Mechanics}, publisher={Springer Science and Business Media LLC}, author={Fuest, Mario and Winkler, Michael}, year={2024} }","mla":"Fuest, Mario, and Michael Winkler. “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing.” Journal of Mathematical Fluid Mechanics, vol. 26, no. 4, 60, Springer Science and Business Media LLC, 2024, doi:10.1007/s00021-024-00899-8.","ieee":"M. Fuest and M. Winkler, “Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing,” Journal of Mathematical Fluid Mechanics, vol. 26, no. 4, Art. no. 60, 2024, doi: 10.1007/s00021-024-00899-8."},"_id":"63254","year":"2024"}