Changes in the mean sea level are the result of climate change, environmental change and human activity. The Baltic Sea is located in an area of glacial isostatic adjustment (GIA) which scientists are particularly interested in. However, published reports from this region do not include tide gauges located on the Polish coast of the Baltic Sea. Previous scientific studies include only selected tide gauges at various time intervals. The authors used different types of data (Revised Local Reference (RLR) data and metric data). They did not analyze the occurrence of vertical shifts (jumps) in time series. The main aim of this article is to determine changes in the mean level of the Baltic Sea at selected tide gauges on the southern Baltic Sea coast. The tide gauge data to determine changes in the mean sea level of the Baltic Sea on the Polish coast for the years 1811-2015, were acquired from the Institute of Meteorology and Water Management – National Research Institute (IMGW–PIB) in Poland and from the PSMSL (Permanent Service for Mean Sea Level) database. In the calculations, metric data, i.e. average monthly values, were used for tide gauges in Świnoujście, Kołobrzeg, Ustka, Stolpmunde, Władysławowo, and Gdańsk. For the reduction of vertical shifts in time series due to a change in the reference level, the author’s proprietary VSED algorithm was applied. Time series were analyzed in terms of seasonality effect. Statistical methods were used to determine the trend: linear regression analysis, spectral analysis, index method. A moving average with a "window" of 19 years was used to smooth the data. Changes in the mean level of the Baltic Sea at the analyzed tide gauges indicate small, short-time positive changes as well as a gradual, slight increase in the mean sea level ranging from +0.8 mm/y to +2.4 mm/y. The best-fitting trend line was obtained when adopting the application of the Fourier function and the moving average with a 19-year window. The analysis of vertical shifts (jumps) showed that there are vertical shifts not revealed at the stage of metric data reduction to the reference level. It has been shown that series from two tide gauges located close to each other can be combined and the series can thus be extended, which results in a reduction in the theoretical error of the determination of the trend.
Motivated by [10], we prove that the upper bound of the density function $\rho $ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.