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GLOBAL SOLUTIONS TO CHEMOTAXIS-NAVIER-STOKES EQUATIONS IN CRITICAL BESOV SPACES.
- Source :
- Discrete & Continuous Dynamical Systems - Series B; Oct2018, Vol. 23 Issue 8, p3427-N.PAG, 34p
- Publication Year :
- 2018
-
Abstract
- In this article, we consider the Cauchy problem to chemotaxis model coupled to the incompressible Navier-Stokes equations. Using the Fourier frequency localization and the Bony paraproduct decomposition, we establish the global-in-time existence of the solution when the gravitational potential ϕ and the small initial data (u0,n0,c0) in critical Besov spaces under certain conditions. Moreover, we prove that there exist two positive constants σ 0 and C0 such that if the gravitational potential ϕ ∈B<subscript>p</subscript><superscript>3</superscript>,/<subscript>1</subscript><superscript>p</superscript> (R<superscript>3</superscript>) and the initial data (u0,n0,c0):=(u<subscript>0</subscript><superscript>1</superscript>,u<subscript>0</subscript><superscript>2</superscript>,u<subscript>0</subscript><superscript>3</superscript>,n0,c0):=(u<subscript>0</subscript><superscript>h</superscript>,u<subscript>0</subscript><superscript>3</superscript>,n0,c0) satisfies . . . for some p; q with , then the global existence results can be extended to the global solutions without any small conditions imposed on the third component of the initial velocity field u<subscript>0</subscript><superscript>3</superscript> in critical Besov spaces with the aid of continuity argument. Our initial data class is larger than that of some known results. Our results are completely new even for three-dimensional chemotaxis-Navier-Stokes system. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15313492
- Volume :
- 23
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Discrete & Continuous Dynamical Systems - Series B
- Publication Type :
- Academic Journal
- Accession number :
- 131844506
- Full Text :
- https://doi.org/10.3934/dcdsb.2018284