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Differential EquationsIncompressible LimitHydrodynamic LimitEvolution EquationsBoltzmann EquationMathematical AnalysisNonlinear Parabolic Partial Differential EquationsFree BoundaryFluid MechanicsGas DynamicsNonlinear SystemsVariational Wave EquationOne-dimensional Euler EquationsNonlinear Fokker-Planck EquationCompressible Viscous FluidsQuasilinear Hyperbolic SystemInitial DataExistence of Weak SolutionNonlinear Parabolic PDEsMathematical Consistency