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The Hele-Shaw semi-flow
Thomas Alazard, Herbert Koch
We prove that the Cauchy problem is well-posed in a strong sense and in a general setting. Our main result is the construction of an abstract semi-flow for the Hele-Shaw problem wi…
math.AP2023
Wellposedness for the KdV hierarchy
Friedrich Klaus, Herbert Koch, Baoping Liu
We prove a version of wellposedness for all equations of the KdV hierarchy in . Ingredients are 1) The Miura map which allows to define the Gardner hierarchy through the ge…