Global weak solution for a chemotaxis Navier–Stokes system with p-Laplacian diffusion and singular sensitivity

Nonlinear Analysis: Real World Applications - Tập 73 - Trang 103898 - 2023
Jiayi Han1, Changchun Liu1
1Department of Mathematics, Jilin University, Changchun 130012, China

Tài liệu tham khảo

Tuval, 2005, Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. USA, 102, 2277, 10.1073/pnas.0406724102 Winkler, 2014, Stabilization in a two-dimensional chemotaxis-Navier–Stokes system, Arch. Ration. Mech. Anal., 211, 455, 10.1007/s00205-013-0678-9 Winkler, 2016, Global weak solutions in a three-dimensional chemotaxis-Navier–Stokes system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 33, 1329, 10.1016/j.anihpc.2015.05.002 Li, 2016, Global boundedness of solutions for the chemotaxis-Navier–Stokes system in R2, J. Differential Equations, 261, 6570, 10.1016/j.jde.2016.08.045 Duan, 2010, Global solutions to the coupled chemotaxis–fluid equations, Comm. Partial Differential Equations, 35, 1635, 10.1080/03605302.2010.497199 Liu, 2011, A coupled chemotaxis–fluid model: global existence, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28, 643, 10.1016/j.anihpc.2011.04.005 Lorz, 2010, Coupled chemotaxis fluid model, Math. Models Methods Appl. Sci., 20, 987, 10.1142/S0218202510004507 Winkler, 2012, Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops, Comm. Partial Differential Equations, 37, 319, 10.1080/03605302.2011.591865 Lankeit, 2016, Long-term behaviour in a chemotaxis–fluid system with logistic source, Math. Models Methods Appl. Sci., 26, 2071, 10.1142/S021820251640008X Winkler, 2019, A three-dimensional Keller–Segel-Navier–Stokes system with logistic source: global weak solutions and asymptotic stabilization, J. Funct. Anal., 276, 1339, 10.1016/j.jfa.2018.12.009 Cong, 2016, A degenerate p-Laplacian Keller–Segel model, Kinet. Relat. Models, 9, 687, 10.3934/krm.2016012 Li, 2020, Global boundedness of weak solution in an attraction–repulsion chemotaxis system with p-Laplacian diffusion, Nonlinear Anal. RWA, 51, 10.1016/j.nonrwa.2019.04.014 Porzio, 2011, Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems, Nonlinear Anal., 74, 5359, 10.1016/j.na.2011.05.020 Zheng, 2021, Global weak solution in a p-Laplacian Keller–Segel system with nonlinear sensitivity and saturation effect, J. Math. Phys., 62, 11, 10.1063/5.0056342 Tao, 2019, Global weak solutions for the three-dimensional chemotaxis-Navier–Stokes system with slow p-Laplacian diffusion, Nonlinear Anal. RWA, 45, 26, 10.1016/j.nonrwa.2018.06.005 Tao, 2020, Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion, J. Differential Equations, 268, 6872, 10.1016/j.jde.2019.11.078 Liu, 2020, Global existence for a chemotaxis-haptotaxis model with p-Laplacian, Commun. Pure Appl. Anal., 19, 1399, 10.3934/cpaa.2020070 Han, 2021, Global existence for a two-species chemotaxis-Navier–Stokes system with p-Laplacian, Electron. Res. Arch., 29, 3509, 10.3934/era.2021050 Du, 2021, Time periodic solution to a two-species chemotaxis-Stokes system with p-Laplacian diffusion, Commun. Pure Appl. Anal., 20, 4321, 10.3934/cpaa.2021162 Liu, 2020, Boundedness in a chemotaxis-(Navier-)Stokes system modeling coral fertilization with slow p-Laplacian diffusion, J. Math. Fluid Mech., 22, 31, 10.1007/s00021-019-0469-7 Liu, 2021, Boundedness in a three-dimensional chemotaxis-Stokes system modeling coral fertilization with arbitrarily slow p-Laplace diffusion, Math. Nachr., 294, 2200, 10.1002/mana.202100103 Zhuang, 2020, Global weak solutions for a 3D chemotaxis-Stokes system with slow p-Laplacian diffusion and rotation, Nonlinear Anal. RWA, 56, 10.1016/j.nonrwa.2020.103163 Zhuang, 2021, Global boundedness of weak solutions to a fully parabolic chemotaxis system with p-Laplacian diffusion and logistic-type source, Z. Angew. Math. Phys., 72, 18, 10.1007/s00033-021-01595-7 Keller, 1971, Traveling bands of chemotactic bacteria: A theoretical analysis, J. Theoret. Biol., 27, 235, 10.1016/0022-5193(71)90051-8 Lankeit, 2017, Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion, J. Differential Equations, 262, 4052, 10.1016/j.jde.2016.12.007 Lankeit, 2019, On the global generalized solvability of a chemotaxis model with signal absorption and logistic growth terms, Nonlinearity, 32, 1569, 10.1088/1361-6544/aaf8c0 Zhou, 2022, Global solvability to a singular chemotaxis-consumption model with fast and slow diffusion and logistic source, Discrete Contin. Dyn. Syst. Ser. B, 27, 2065, 10.3934/dcdsb.2021122 Pang, 2021, Asymptotic profile of a two-dimensional Chemotaxis-Navier–Stokes system with singular sensitivity and logistic source, Math. Models Methods Appl. Sci., 31, 577, 10.1142/S0218202521500135 Ren, 2020, Global boundedness of solutions to a chemotaxis–fluid system with singular sensitivity and logistic source, Commun. Pure Appl. Anal., 19, 3843, 10.3934/cpaa.2020170 Wu, 2020, Boundedness and asymptotic behavior to a chemotaxis–fluid system with singular sensitivity and logistic source, J. Math. Anal. Appl., 484, 10.1016/j.jmaa.2019.123748 Stinner, 2014, Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion, SIAM J. Math. Anal., 46, 1969, 10.1137/13094058X Jin, 2018, Boundedness and global solvability to a chemotaxis-haptotaxis model with slow and fast diffusion, Discrete Contin. Dyn. Syst. Ser. B, 23, 1675 Winkler, 2010, Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model, J. Differential Equations, 248, 2889, 10.1016/j.jde.2010.02.008 Winkler, 2015, Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity, Calc. Var. Partial Differential Equations, 54, 3789, 10.1007/s00526-015-0922-2 Ishida, 2014, Boundedness in quasilinear Keller–Segel systems of parabolic-parabolic type on non-convex bounded domains, J. Differential Equations, 256, 2993, 10.1016/j.jde.2014.01.028 Zheng, 2022, Global existence and boundedness in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity, Ann. Mat. Pura Appl., 201, 243, 10.1007/s10231-021-01115-4 Lions, 1969