Displaying similar documents to “Ill-posed Cauchy problems for ideal gas equations and their regularization”

Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum

Huanyuan Li (2023)

Applications of Mathematics

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This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent...

Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

Daniele Andreucci, Marianne K. Korten (1993)

Revista Matemática Iberoamericana

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The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1 loc (Rn x (0,T)) to (0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)), for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection...