Mathematics – Analysis of PDEs
Scientific paper
2010-01-24
Mathematics
Analysis of PDEs
21 pp. Version 4 withdrawn due to an error. Submitted to Differential and integral equations
Scientific paper
We present a technique for derivation of a priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to evolutionary partial differential equations of hydrodynamic type. It involves a transformation of the flow velocity in the Fourier space, which introduces a feedback between the index of the norm and the norm of the transformed solution, and results in emergence of a mildly dissipative term. To illustrate the technique, we derive finite-time bounds for Gevrey-Sobolev norms of solutions to the Euler and inviscid Burgers equations, and global in time bounds for the Voigt-type regularisations of the Euler and Navier-Stokes equation (assuming that the respective norm of the initial condition is bounded). The boundedness of the norms implies analyticity of the solutions in space.
No associations
LandOfFree
A priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to equations of hydrodynamic type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to equations of hydrodynamic type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A priori bounds for Gevrey-Sobolev norms of space-periodic three-dimensional solutions to equations of hydrodynamic type will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-696744