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In this paper, we consider the 3-D compressible isentropic radiation hydrodynamics (RHD) equations. The local existence of strong solutions with vacuum is firstly established when the initial data is arbitrarily large, contains vacuum and…
We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\infty$ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the…
We consider the 3D isentropic compressible Euler equations with the ideal gas law. We provide a constructive proof of shock formation from smooth initial datum of finite energy, with no vacuum regions, with nontrivial vorticity present at…
For the Euler equations of isentropic gas dynamics in one space dimension, also knowns as p-system in Lagrangian coordinate, it is known that the density can be arbitrarily close to zero as time goes to infinity, even when initial density…
Consider the characteristic initial value problem for the Einstein vacuum equations without any symmetry assumptions. Impose a sequence of data on two intersecting null hypersurfaces, each of which is foliated by spacelike $2$-spheres.…
We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density. The central feature of the solutions is the…
In this paper, we give a new proof to a past stability result established in Fournodavlos-Rodnianski-Speck (arXiv:2012.05888), for Kasner solutions of the $(3+1)$-dimensional Einstein vacuum equations under polarized $U(1)$-symmetry. Our…
We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…
We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main…
We study the formation of singularity for the isothermal Euler-Poisson system arising from plasma physics. Contrast to the previous studies yielding only limited information on the blow-up solutions, for instance, sufficient conditions for…
In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin.…
The Carrollian fluid equations arise from the equations for relativistic fluids in the limit as the speed of light vanishes, and have recently experienced a surge of interest in the theoretical physics community in the context of asymptotic…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
We study the Cauchy problem for the $3D$ compressible Euler equations under an arbitrary equation of state with positive speed of sound, aside from that of a Chaplygin gas. For open sets of smooth initial data with non-trivial vorticity and…
A class of semi-bounded solutions of the two-dimensional incompressible Euler equations satisfying either periodic or Dirichlet boundary conditions is examined. For smooth initial data, new blowup criteria in terms of the initial concavity…
We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an…
Classical vorticity solution branches of the three dimensional incompressible Euler equation are constructed where a velocity component can blow up at some point after finite time for regular data in H2. Furthermore, vorticity can blow up…
We analyze existence and properties of solutions of two-dimensional general relativistic initial data sets with a negative cosmological constant, both on spacelike and characteristic surfaces. A new family of such vacuum, spacelike data…
We provide a new existence result for weak solutions to the one-dimensional Euler equations with a maximal density constraint, corresponding to a unilateral constraint on the density. Such models arise in the description of congestion…
In this paper, we consider the Cauchy problem of the isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum in $\mathbb{R}$, where the viscosity depends on the density in a super-linear power law(i.e.,…