Dynamics of Partial Differential Equations
Volume 13 (2016)
Remarks on ill-posedness for the Dirac–Klein–Gordon system
Pages: 179 – 190
We show ill-posedness of the Cauchy problem for the Dirac–Klein–Gordon system in one spatial dimension with some indices of the Sobolev spaces which the initial data belong to. By combining with the existing papers, we define the entire range of those indices for well-posedness or ill-posedness with the exception of one point. At this point, it is still unsolved whether well-posedness holds or not with respect to Sobolev spaces. We introduce one solvability for the problem of this point by giving the result of the unique existence of solution in the corresponding Lebesgue spaces.
Dirac–Klein–Gordon system, Cauchy problem, well-posedness, ill-posedness
2010 Mathematics Subject Classification
35B30, 35Q41, 35R25