论文题目:GLOBAL WELLPOSDENESS TO INCOMPRESSIBLE INHOMOGENEOUS FLUID SYSTEM WITH BOUNDED DENSITY AND NON-LIPSCHITZ VELOCITY
论文作者:JINGCHI HUANG, MARIUS PAICU, AND PING ZHANG(张平)
发表期刊:AMS
论文摘要:In this paper, we first prove the global existence of weak solutions to the d-imensional incompressible inhomogeneous Navier-Stokes equations with initial data a0 ∈ L∞(Rd), u0 =(uh0 , ud0) ∈ ˙B−1+dpp,r (Rd), which satisfies μka0kL1 + kuh0 k˙B−1+ dpp,r expCrμ−2rkud 0k2r ˙B −1+ dpp,r ≤ c0μ for some positive constants c0,Cr 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 field.Furthermore, with additional regularity assumption on the initial velocity or on the initial density,we can also prove the uniqueness of such solution. We should mention that the classical maximal Lp(Lq) regularity theorem for the heat kernel plays an essential role in this context.
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