GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE IN

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We prove the global existence of classical solutions to a fluid-particle interaction model in R3,namely,compressible Navier-Stokes-Smoluchowski equations,when the initial data are close to the stationary state (ρ*,0,η*) and the extal potential satisfies the smallness assumption.Furthermore,optimal decay rates of classical solutions in Ha-framework are obtained.
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