TY - JOUR
T1 - Dispersive estimates for the stably stratified boussinesq equations
AU - Lee, Sanghyuk
AU - Takada, Ryo
N1 - Funding Information:
Acknowledgements. The first author is supported in part by the National Research Foundation of Korea (grant no. NRF-2015R1A4A1041675). The second author is partially supported by JSPS KAKENHI (grant no. JP15H05436).
PY - 2017
Y1 - 2017
N2 - We consider the initial value problem for the 3D Boussinesq equations for stably stratified fluids without the rotational effect. We establish the sharp dispersive estimate for the linear propagator related to the stable stratification. As an application, we give the explicit relation between the size of initial data and the buoyancy frequency which ensures the unique existence of global solutions to our system. In particular, it is shown that the size of the initial thermal disturbance can be taken in proportion to the strength of stratification.
AB - We consider the initial value problem for the 3D Boussinesq equations for stably stratified fluids without the rotational effect. We establish the sharp dispersive estimate for the linear propagator related to the stable stratification. As an application, we give the explicit relation between the size of initial data and the buoyancy frequency which ensures the unique existence of global solutions to our system. In particular, it is shown that the size of the initial thermal disturbance can be taken in proportion to the strength of stratification.
UR - http://www.scopus.com/inward/record.url?scp=85038851658&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85038851658&partnerID=8YFLogxK
U2 - 10.1512/iumj.2017.66.6179
DO - 10.1512/iumj.2017.66.6179
M3 - Article
AN - SCOPUS:85038851658
VL - 66
SP - 2037
EP - 2070
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
SN - 0022-2518
IS - 6
ER -