Well-posedness and ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces

DOI10.1016/j.na.2020.111782zbMath1442.35006OpenAlexW3006247116MaRDI QIDQ1988400

Yao Nie, Jia Yuan

Publication date: 23 April 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.111782

zbMATH Keywords

well-posednessBesov spacesill-posednesschemotaxis modelnorm inflation

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell movement (chemotaxis, etc.) (92C17) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Related Items (6)

Local and global solvability for Keller-Segel system in Besov-Morrey spaces ⋮ Ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces ⋮ Ill-posedness issue on a multidimensional chemotaxis equations in the critical Besov spaces ⋮ Global existence of large solutions for the parabolic-elliptic Keller-Segel system in Besov type spaces ⋮ Ill-posedness of the hyperbolic Keller-Segel model in Besov spaces ⋮ Ill-posedness issue for a multidimensional hyperbolic-parabolic model of chemotaxis in critical Besov spaces \(\dot{B}_{2 d , 1}^{- \frac{ 3}{ 2}} \times ( \dot{B}_{2 d , 1}^{- \frac{ 1}{ 2}} )^d\)

Cites Work

• Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations
• Global well-posedness for Keller-Segel system in Besov type spaces
• Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Traveling bands of chemotactic bacteria: a theoretical analysis
• Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity
• Local existence and finite time blow-up of solutions in the 2-D Keller-Segel system
• Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level.
• A user's guide to PDE models for chemotaxis
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Symmetrization techniques on unbounded domains: Application to a chemotaxis system on \(\mathbb{R}^N\)
• From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
• Global existence in critical spaces for compressible Navier-Stokes equations
• A chemotaxis model motivated by angiogenesis
• Optimal condition for non-simultaneous blow-up in a reaction-diffusion system
• Global well-posedness for a multidimensional chemotaxis model in critical Besov spaces
• Global well-posedness of coupled parabolic systems
• Navier-Stokes equation with variable density and viscosity in critical space
• On the uniqueness in critical spaces for compressible Navier-Stokes equations
• On the ill-posedness of the compressible Navier-Stokes equations in the critical Besov spaces
• Global Dynamics of a Hyperbolic-Parabolic Model Arising from Chemotaxis
• Nonlinear Stability of Traveling Waves to a Hyperbolic-Parabolic System Modeling Chemotaxis
• Fourier Analysis and Nonlinear Partial Differential Equations
• NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC–PARABOLIC SYSTEM ARISING IN CHEMOTAXIS
• Nonlinear PDEs
• ON A HYPERBOLIC–PARABOLIC SYSTEM MODELING CHEMOTAXIS
• Global well-posedness for compressible Navier-Stokes equations with highly oscillating initial velocity
• Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Nonlinear Analysis - Theory and Methods
• Unnamed Item
• Unnamed Item

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