Springer Almost Global Solutions Of Capillary-Gravity Water Waves Equations On The Circle

Name: Springer Almost Global Solutions Of Capillary-Gravity Water Waves Equations On The Circle
Brand: Springer
Price: 39.99 GBP
Availability: InStock

Springer Almost Global Solutions Of Capillary-Gravity Water Waves Equations On The Circle thumbnail

Price Alert

★ 4.9

£39.99

Best price from link.springer.com

Price Alert

★ 4.9

£39.99

Best price from link.springer.com

Price Alert

★ 4.9

£39.99

Best price from link.springer.com

Price Alert

★ 4.9

£39.99

Best price from link.springer.com

binding

Price details

Lowest price for a new Springer Almost Global Solutions Of Capillary-Gravity Water Waves Equations On The Circle is £39.99. This is currently the cheapest offer among 1 stores.

Product Information

The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations,we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.

Reviews

0,0

No Ratings Yet

Be the first to share your experience with this product!

You might also like

We couldn't find any suggested products right now.

Springer Almost Global Solutions Of Capillary-Gravity Water Waves Equations On The Circle

Price details

Product Information

Reviews

You might also like

Stores selling this product

Subscribe to our newsletter

PriceRadar

Product Information

Reviews

You might also like