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We are concerned with a 3D chemotaxis model arising from biology, which is a coupled hyperbolic-parabolic system. We prove the global existence of a strong solution when H2-norm of the initial perturbation around a constant state is sufficiently small. Moreover, if additionally, L1-norm of the initial perturbation is bounded; the optimal convergence rates are also obtained for such a solution. The proofs are obtained by combining spectral analysis with energy methods

journal of applied mathematics

Global Existence and Convergence Rates for the Strong Solutions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>to the 3D Chemotaxis Model

Global Existence and Convergence Rates for the Strong Solutions inH2to the 3D Chemotaxis Model