Global well-posedness for a multidimensional chemotaxis model in critical Besov spaces

DOI10.1007/s00033-012-0193-0zbMath1258.35195OpenAlexW2111764281MaRDI QIDQ1938475

Cheng Chun Hao

Publication date: 4 February 2013

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-012-0193-0

zbMATH Keywords

Cauchy problemcritical Besov spacesglobal well-posednesschemotaxis model

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Initial value problems for systems of nonlinear higher-order PDEs (35G55) Initial value problems for mixed-type systems of PDEs (35M31)

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Cites Work

• Unnamed Item
• Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
• Initiation of slime mold aggregation viewed as an instability
• Model for chemotaxis
• Traveling bands of chemotactic bacteria: a theoretical analysis
• Global solutions of some chemotaxis and angiogenesis system in high space dimension
• Cauchy problem for viscous rotating shallow water equations
• 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
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• About Lifespan of Regular Solutions of Equations Related to Viscoelastic Fluids
• 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
• ON A HYPERBOLIC–PARABOLIC SYSTEM MODELING CHEMOTAXIS
• Global existence of solutions to a hyperbolic-parabolic system
• Shock formation in a chemotaxis model
• A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks
• Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
• Global existence in critical spaces for flows of compressible viscous and heat-conductive gases