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• W2038592893 abstract "In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier–Stokes equations with initial data $${a_0 in L^infty (mathbb{R}^d), u_0 = (u_0^h, u_0^d) in dot{B}^{-1+frac{d}{p}}_{p, r} (mathbb{R}^d)}$$ , which satisfy $${(mu | a_0 |_{L^infty} + |u_0^h|_{dot{B}^{-1+frac{d}{p}}_{p, r}}) {rm exp}(C_r{mu^{-2r}}|u_0^d|_{dot{B}^{-1+frac{d}{p}}_{p,r}}^{2r}) leqq c_0mu}$$ for some positive constants c 0, C r and 1 < p < d, 1 < r < ∞. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity fields. Furthermore, with additional regularity assumptions on the initial velocity or on the initial density, we can also prove the uniqueness of such a solution. We should mention that the classical maximal L p (L q ) regularity theorem for the heat kernel plays an essential role in this context." @default.
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• W2038592893 date "2013-04-04" @default.
• W2038592893 modified "2023-10-16" @default.
• W2038592893 title "Global Well-posedness of Incompressible Inhomogeneous Fluid Systems with Bounded Density or Non-Lipschitz Velocity" @default.
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• W2038592893 doi "https://doi.org/10.1007/s00205-013-0624-x" @default.
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