Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations

By A. Zlotnik. 2000

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Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equations (2010, unknown): “4 ( [30]) Let the function y satisfy y′(t) = g(y) + b′(t) on [0, T ], y(0) = y, with g ∈ C(R) and y, b ∈ W 1,1(0, T ).”
Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier–Stokes Equations with Vacuum (2013, background): “p(R2), which, along with (2.11), gives (2.12). The proof of Lemma 2.5 is completed. Next, to get the uniform(in time) upperboundof the density ρ, we need the following Zlotnik inequality. Lemma 2.6 ( [34]) Let the function y satisfy y′(t) = g(y) +b′(t) on [0,T], y(0) = y0, with g ∈ C(R) and y,b ∈ W1”
Some uniform estimates and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows (2006, unknown): “4 ([27]) Let the function y satisfy y′(t) ≤ g(y) + b′(t) on [0, T ], y(0) = y, with g ∈ C(R) and y, b ∈W 1,1(0, T ).”