Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in \(\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}\)

DOI10.3934/dcds.2014.34.437zbMath1368.76013arXiv1302.5785OpenAlexW2326966679MaRDI QIDQ379718

Chao Deng, Xiao Hua Yao

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5785

zbMATH Keywords

ill-posednesswellposednessgeneralized Navier-Stokes equationsTriebel-Lizorkin space

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Fractional partial differential equations (35R11)

Related Items (9)

Ill-posedness of the two-dimensional Keller-Segel model in Triebel-Lizorkin spaces ⋮ Global well-posedness for fractional Navier-Stokes equations in variable exponent Fourier-Besov-Morrey spaces ⋮ Well/ill-posedness for the dissipative Navier-Stokes system in generalized Carleson measure spaces ⋮ Global well-posedness of generalized magnetohydrodynamics equations in variable exponent Fourier-Besov-Morrey spaces ⋮ Global well-posedness of the incompressible fractional Navier-Stokes equations in Fourier-Besov spaces with variable exponents ⋮ Global well-posedness and long time decay of fractional Navier-Stokes equations in Fourier-Besov spaces ⋮ Algebra properties in Fourier-Besov spaces and their applications ⋮ Global large solutions to the 3-D generalized incompressible Navier-Stokes equations ⋮ Global well-posedness for the fractional Boussinesq-Coriolis system with stratification in a framework of Fourier-Besov type

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