Context : Magnetic neutral points are potential locations for energy conversion in the solar corona .
2D X-points have been widely studied in the past , but only a few of those studies have taken finite plasma beta effects into consideration , and none of them look at the dynamical evolution of the system .
At the moment there exists no description of the formation of a non-force-free equilibrium around a two-dimensional X-point .

Aims : Our aim is to provide a valid magnetohydrostatic equilibrium from the collapse of a 2D X-point in the presence of a finite plasma pressure , in which the current density is not simply concentrated in an infinitesimally thin , one-dimensional current sheet , as found in force-free solutions .
In particular , we wish to determine if a finite pressure current sheet will still involve a singular current , and if so , what is the nature of the singularity .

Methods : We use a full MHD code , with the resistivity set to zero , so that reconnection is not allowed , to run a series of experiments in which an X-point is perturbed and then is allowed to relax towards an equilibrium , via real , viscous damping forces .
Changes to the magnitude of the perturbation and the initial plasma pressure are investigated systematically .

Results : The final state found in our experiments is a “ quasi-static ” equilibrium where the viscous relaxation has completely ended , but the peak current density at the null increases very slowly following an asymptotic regime towards an infinite time singularity .
Using a high grid resolution allows us to resolve the current structures in this state both in width and length .
In comparison with the well known pressureless studies , the system does not evolve towards a thin current sheet , but concentrates the current at the null and the separatrices .
The growth rate of the singularity is found to be t ^ { D } , with 0 < D < 1 .
This rate depends directly on the initial plasma pressure , and decreases as the pressure is increased .
At the end of our study , we present an analytical description of the system in a quasi-static non-singular equilibrium at a given time , in which a finite thick current layer has formed at the null .
The dynamical evolution of the system and the dependence of the final state on the initial plasma and magnetic quantities is discussed , as are the energetic consequences .

Conclusions :