Unconditional Well-Posedness In the Energy Space For The Ginzburg-Landau Equation.

We prove new type of conservation laws and unconditional well-posedness in the energy space for the solution to the Ginzburg-Landau equation with complex pure power nonlinearity. The main tools used are an approach unfolding the conservation of mass and energy as basically independent from the regularity of the solution in combination with classical Strichartz estimates and a new extended Strichartz estimates. [ABSTRACT FROM AUTHOR]