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.
Classical Euler flows generate the strong Guderley imploding shock wave
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Derives a boundedness-based continuation criterion for the Landau-Coulomb equation that rules out Type II approximately self-similar blow-ups slower than Type I without decay assumptions on the inner profile.
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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On Hydrodynamic Implosions and the Landau-Coulomb Equation
Derives a boundedness-based continuation criterion for the Landau-Coulomb equation that rules out Type II approximately self-similar blow-ups slower than Type I without decay assumptions on the inner profile.
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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.