Global well-posedness for the 2D stable Muskat problem in $H^{3/2}$
Diego Córdoba, Omar Lazar
Abstract
We prove a global existence result of a unique strong solution in Ḣ5/2 ∩ Ḣ3/2 with small Ḣ3/2 semi-norm for the 2D Muskat problem, hence allowing the interface to have arbitrary large finite slopes and finite energy (thanks to the L 2 maximum principle).The proof is based on the use of a new formulation of the Muskat equation that involves oscillatory terms.Then, a careful use of interpolation inequalities in homogeneneous Besov spaces allows us to close the a priori estimates.
Topics & Concepts
MathematicsApplied mathematicsMathematical analysisAdvanced Mathematical Physics ProblemsNavier-Stokes equation solutionsComputational Fluid Dynamics and Aerodynamics