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Abstract: We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is al...
Abstract: It is shown that Wiener's regularity of the vertex of a backward paraboloid for 3D Navier-Stokes equations with zero Dirichlet conditions on the paraboloid boundary is given by Petrovskii's ...
Abstract: We consider the spectral stability of solitary wave solutions \phi(x)e^{-i\omega t} to the nonlinear Dirac equation in any dimension. This equation is well-known to theoretical physicists as...
We investigate the dynamics of travelling oscillating solitons of the cubic NLS equation under an external spatiotemporal forcing of the form $f(x,t) = a \exp[iK(t)x]$. For the case of time-independen...
We prove a geometric criterion on a SL(2,R)-invariant ergodic probability measure on the moduli space of holomorphic abelian differentials on Riemann surfaces for the non-uniform hyperbolicity of the ...
We introduce a notion of local tropical variety which is a straightforward extension of tropism introduced by Maurer, and prove a variant of the fundamental theorem of tropical algebraic geometry in s...

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