2 problems
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Liu's asymptotic porous-medium conjecture for damped Euler equations
Liu's conjecture. Solutions of the Euler equations with damping should behave asymptotically like solutions of the porous media equation.
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Liu's convergence conjecture for damped Euler flows in vacuum
The Euler system with damping is considered in a vacuum free-boundary setting, where the density may vanish at the fluid boundary and the physical vacuum condition describes the co…