The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation

الملخص EN

The existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space C([0,T);Hs(R)) ∩C1([0,T);Hs-1(R)) provided that the initial value lies in Hs(R) with s>3/2.

Meanwhile, we prove the existence of global weak solutions in L∞([0,∞);L2(R)) for the equation.