New smooth self-similar implosion profiles for compressible Euler equations are constructed with explicit exponents and proven stable under radial and certain non-radial perturbations.
Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases
4 Pith papers cite this work. Polarity classification is still indexing.
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For every d≥3 and every α<1−2/d, axisymmetric swirl-free incompressible Euler admits self-similar blow-up solutions with C^{1,α} initial velocity that is smooth away from the origin.
Global well-posedness of regular solutions to barotropic compressible Navier-Stokes with density-dependent viscosities ρ^δ (δ ∈ (1/2,1)) for large spherical symmetric data vanishing at infinity in 2 and 3 dimensions.
New weighted L^∞ a priori bound for inhomogeneous Landau and Boltzmann equations yields a hydrodynamic-independent continuation criterion and obstructs lifting of 3D Euler singularities.
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Smooth and stable Euler implosions
New smooth self-similar implosion profiles for compressible Euler equations are constructed with explicit exponents and proven stable under radial and certain non-radial perturbations.
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Self-similar blow-up solutions of $d$-dimensional incompressible Euler equations with $C^{1,\left(1-2/d\right)-}$ velocity
For every d≥3 and every α<1−2/d, axisymmetric swirl-free incompressible Euler admits self-similar blow-up solutions with C^{1,α} initial velocity that is smooth away from the origin.
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Global Regular Solutions of the Compressible Navier-Stokes Equations with Nonlinear Density-Dependent Viscosities and Large Initial Data of Spherical Symmetry
Global well-posedness of regular solutions to barotropic compressible Navier-Stokes with density-dependent viscosities ρ^δ (δ ∈ (1/2,1)) for large spherical symmetric data vanishing at infinity in 2 and 3 dimensions.
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Pointwise bounds and obstructions to blowup for the Landau and Boltzmann equations
New weighted L^∞ a priori bound for inhomogeneous Landau and Boltzmann equations yields a hydrodynamic-independent continuation criterion and obstructs lifting of 3D Euler singularities.