Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation
Tsukasa Iwabuchi
Abstract
This paper is concerned with the Cauchy problem of the Burgers equation with the critical dissipation. The well-posedness and analyticity in both of the space and the time variables are studied based on the frequency decomposition method. The large time behavior is revealed for any large initial data. As a result, it is shown that any smooth and integrable solution is analytic in space and time as long as time is positive and behaves like the Poisson kernel as time tends to infinity. The corresponding results are also obtained for the quasi-geostrophic equation.
Topics & Concepts
Burgers' equationDissipationGeostrophic windPhysicsClassical mechanicsMathematical physicsMathematical analysisMathematicsMechanicsPartial differential equationThermodynamicsNavier-Stokes equation solutionsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential Equations