I wonder if a semistalbe K3 surface over a $p$-adic field has a minimal semistable model. I guess yes but I do not find any reference. 


Also, if we have a semistable K3 surface with a log structure, there exist a minimal log semistable model? 


Thanks. 



Minimal semistable model for K3-surfaces.
The answer is yes when p>3. Look at Kawamata's paper


Semistable minimal models of threefolds in positive or mixed characteristic.
J. Algebraic Geom. 3 (1994), no. 3, 463–491. 


and a correction in


Index 1 covers of log terminal surface singularities. 
J. Algebraic Geom. 8 (1999), no. 3, 519–527. 


